Fifa president Sepp Blatter has apologised to the Football Association over Frank Lampard's disallowed goal in England's World Cup defeat by Germany.
Blatter said the error had convinced him to reopen the debate on goal-line technology at a board meeting in July.
Lampard was denied a goal in Sunday's 4-1 second-round loss, even though his shot clearly crossed the line.
Blatter also said sorry to Mexico after Carlos Tevez's offside goal was allowed to stand in Argentina's 3-1 victory.
Uruguayan referee Jorge Larrionda, who missed Lampard's goal, and Italian referee Roberto Rosetti, who allowed Tevez's offside Argentina goal to stand, have not been retained for the remainder of the tournament.
Lampard's strike came during a spell of England dominance and would have levelled the score at 2-2.
Fifa president Sepp Blatter
Blatter reopens door to technology in football
The high-profile error sparked a clamour for referees to be given more assistance, with international players' union FifPro leading calls for goal-line technology to be introduced.
Blatter said the issue will now form part of the agenda at next month's meeting of the International FA Board (IFAB), the body that decides the laws of the game.
"It is obvious that after the experiences so far at this World Cup it would be a nonsense not to reopen the file on goal-line technology," stated Blatter.
The Tevez goal - the first in Argentina's win on Sunday - was replayed on the screens in the stadium, sparking angry clashes between officials and the Mexican players and coaches.
"Personally I deplore it when you see evident referee mistakes but it's not the end of a competition or the end of football, this can happen," added Blatter.
"Yesterday I spoke to the two federations [England and Mexico] directly concerned by referees' mistakes.
The referee waves the Mexico and Argentina players away
Tevez puts Argentina into controversial lead
"I have expressed to them apologies and I understand they are not happy and that people are criticising.
"We will naturally take on board the discussion on technology and have the first opportunity in July at the business meeting."
Blatter's call comes less than four months after Fifa general secretary Jerome Valcke said the door was "closed" on goal-line technology and video replays after a vote by the IFAB.
The decision was reached after watching presentations of two systems - Cairos, a microchip inserted in a ball, and Hawk-Eye, which is used in tennis and cricket.
In a statement on Fifa's website after the verdict, Blatter argued that human errors were part of football's appeal.
"The game must be played in the same way no matter where you are in the world," he wrote. "The simplicity and universality of the game is one of the reasons for its success.
"No matter which technology is applied, at the end of the day a decision will have to be taken by a human being. This being the case, why remove the responsibility from the referee to give it to someone else?"
The Fifa chief was in the crowd at Free State Stadium in Bloemfontein as referee Jorge Larrionda and his assistant Mauricio Espinosa failed to spot that Lampard's 38th-minute shot had dropped well over the line.
German media have claimed the incident atones for the 1966 final when Geoff Hurst's strike for England against West Germany was allowed to stand, even though it was unclear whether the whole of the ball had crossed the line.
"It happened in 1966 and then 44 years later - though it was not quite the same," added Blatter.
"I apologised to England and Mexico. The English said thank you and accepted that you can win some and you lose some and the Mexicans bowed their head and accepted it."
Former FA chief executive Brian Barwick, a long-term advocate of goal-line technology, said the stakes are too high for Fifa to go on resisting practices which are now an accepted part of sports like cricket and tennis.
Sepp Blatter
Blatter has always argued for football to retain its human element
"When you get a game in the last 16 of the World Cup and England are 2-1 down, who knows where that game would have gone?" Barwick told BBC Sport.
"The goal was a goal, everybody in my house jumped up at the same time. If eyesight is not going to work, why not help the guys who are on the field and on the touchline?
"Within seconds, via a replay, hundreds of millions of people knew England had scored a legitimate goal. Four people didn't, and those are the men in the middle. These guys needs help. That was a terrible error of judgement."
English World Cup referee Howard Webb, who officiated in last month's Champions League final, said he would be in favour of technological aids if they helped referees make the right call.
"I'm open-minded about anything that makes us more credible as match officials," said Webb.
"Whatever tools I am given I will use them to the best of my ability, and I will use all the experience I have to try to come to the correct decisions.
"I certainly don't feel in any way at all that additional assistance will undermine my position.
"We work closely in England with the officials from other sports, rugby union, rugby league and cricket, we try to learn good practice from them.
"But we have to consider that we are dealing in different sports, football is uniquely fluid in the way that it is played and we need to take care that we don't change that fact. We need to protect the basic way the game is played."
Blatter confirmed the IFAB would only look at the use of technology for goal-line situations, meaning no help for assistant referees over offside decisions like the Tevez goal.
"Football is a game that never stops and the moment there was a discussion if the ball was in or out, or there was a goalscoring opportunity, do we give a possibility to a team to call for replays once or twice like in tennis?
"For situations like the Mexico game you don't need technology."
Blatter also announced that Fifa will be launching a new drive to improve refereeing standards at the top level later this year.
"We will come out with a new model in November on how to improve high level referees," he commented.
"We will start with a new concept of how to improve match control. I cannot disclose more of what we are doing but something has to be changed."
Bookmarks