Manchester City boss Manuel Pellegrini described his decision to stick with Joe Hart in goal for their 3-1 victory over Everton as "very difficult".
There were doubts over the 26-year-old's position after he was culpable for two of Bayern Munich's goals in City's Champions League defeat on Wednesday.
It is not the first time recently that Hart has made high-profile mistakes, and Pellegrini pointedly failed to confirm whether he would pick Hart for the clash with the Toffees in the build-up to the game.
The City stopper got his hand to Romelu Lukaku's shot in the 16th minute but could not keep it out.
Pellegrini did not blame Hart, saying: "Always the responsibility for the goal is with the whole team."
But asked about his decision to choose Hart ahead of Costel Pantilimon, Pellegrini said: "It wasn't a simple decision, it was a very difficult decision, but I think Joe needs the trust of all of us - of me, the other players and the fans.
"Of course he feels he didn't do well the last game, he feels that he was guilty, but it was more important that he reflected how strong his character is."
Everton appealed for a penalty in the first half when Lukaku felt he was pushed over by Matija Nastasic.
James Milner, meanwhile, was perhaps a little fortunate to get away with a yellow card for a strong challenge on James McCarthy just before the break, although Martinez declined to say whether he thought it should have been red.
The Spaniard said: "My overall disappointment is that the game wasn't controlled at all by the referee.
"There was an incident before we conceded the second goal where Seamus Coleman got involved with Alvaro Negredo, there was an argument.
"There were three players out of the action and you need to see that as a referee and do something about it.
"Then the penalty - if that's a penalty, it's going to be an impossible game. There's contact but there's no impeding. That should never be a penalty, and he didn't have the consistency to give a penalty for Lukaku and Nastastic."
Pellegrini felt discussion of the referee's performance was incidental to the result, saying: "I never talk about referees but I am sure the difference between Manchester City and Everton was not the referee.
"They had just one chance to score. We scored three goals and we had four or five other chances."
The defeat was Martinez's first in charge of Everton in the Premier League, and he rued City's swift response after Lukaku had given the visitors the lead.
"I thought we started really bright and we wanted to score the first goal," said Martinez.
"I thought it was important. We couldn't keep the lead long enough. I thought those five or 10 minutes after scoring would have been very important to affect the rest of the performance.
"Conceding was a little bit of a blow but still I saw it as a very open game, a fascinating game of football. From that point on I do feel the referee didn't allow the two teams to compete eye to eye.
"If you concede three goals it makes it very difficult to get a result at a place like this."