Manchester City boss Roberto Mancini was at a loss to explain his side's defeat at Everton after seeing his side throw away a 1-0 lead.
City were frustrated in their Champions League push as the Toffees came from behind to deny them a victory that would all but have secured a Premier League top-four place.
Mancini said: "It was incredible we lost this game. We dominated in the first half and had four or five chances to score.
"But this is football. If you lose concentration, if you concede a yard to the other team, it is difficult.
"A game like this we should never lose. If we want to become a strong team, we cannot lose this game.
"We shouldn't lose it because we had more chances to score in the second half. It is not important who scores the goals, it is important the team wins the game."
Barry was rested as a precaution after a knock while Tevez now has just Tuesday's crunch clash against Champions League-chasing rivals Tottenham to prove his fitness for next week's FA Cup final.
Mancini said of Tevez: "He will need to train with the team and in the next days we will see if it is possible.
"If he can play 20 minutes somehow we can see if he can play or not. At the moment I think 50% for the final."
Mancini and opposite number David Moyes played down a spat involving personnel from both sides at the end of the game.
Tim Cahill and Aleksandar Kolarov appeared to exchange words while Phil Neville was involved in heated discussion with Mancini and his assistant Brian Kidd.
When asked what sparked the incident, Mancini said: "I don't know because I wanted to take off Kolarov. I don't know what upset them."
Moyes said: "It wasn't Phil Neville. I think one of their players said Seamus Coleman had elbowed them or something like that, but it was nothing.
"All the fighting was done in the 90 minutes, not after the game."
With David Silva dominating proceedings for City and Toure scoring after 28 minutes, Moyes admitted his side could have been out of the game by the interval.
He said: "They bossed the game and we never laid a glove on them.
"We were fortunate to go in at half-time 1-0 down.
"We changed the system round a little bit at half-time and I don't know if it was the system but we got closer to people, looked more attacking and were a bigger threat.
"We set out to try to contain Man City but it is very difficult to contain David Silva.
"I think he is as good as anyone in the Premier League at the moment."
Moyes was pleased with the way Everton held on after turning the game around with two goals in the space of seven minutes just after the hour.
He added: "The team Man City had could probably play in the NBA.
"It was like the New York Knicks with the size of them. It was really difficult to match them.
"It was a case of everybody manning the pumps to get us through the last five or six minutes."