Wenger had slammed Arsenal's "suicidal defending" which cost them in a 3-1 home defeat by Monaco in the first leg of their Champions League last-16 clash on Wednesday.
There was, though, no repeat against the Toffees at the Emirates Stadium as Olivier Giroud, who missed several chances in midweek, netted a fine volley on 39 minutes, with a late deflected effort from substitute Tomas Rosicky securing all three points to make the most of Manchester City's defeat at Liverpool earlier on Sunday.
"It was vital for us, for the rest of the season, to win the game today," said Wenger, whose side are now just four points behind City and one ahead of Manchester United.
"What was very important was that we had a mentally united response and we showed that
We are proud of the response that we showed.
"Our defensive concentration was at a much higher level than on Wednesday night.
"We know that we can do better with the ball, but overall what was important for us was to respond with a win.
"We got it and not everybody can produce that after such a disappointment."
Wenger felt his side had answered questions over a perceived lack of leadership.
"I can understand that we got this kind of criticism after the game because it looked like that, but it's not permanent," he said.
"It can sometimes be occasional that not everybody is focused on the right things in the game.
"I believe that we wanted to make the difference too much in the first game [against Monaco] and forgot our basics to defend as a unit.
"Today we came back to our basics and that was very important to find our confidence back."
Wenger had given Gabriel Paulista his first Premier League start, with centre-back Per Mertesacker left on the bench along with England duo Danny Welbeck and Theo Walcott.
The Gunners' boss had no hesitation in giving Giroud another chance in attack.
"When a guy misses one game, straight away to take him out [would be harsh] and I thought his presence would be important against Everton," said Wenger, who confirmed midfielder Francis Coquelin had suffered a broken nose following an accidental clash of heads with French striker Giroud in the second half.
"Olivier's great quality is when his back's to the wall - he has the personality and the character to respond.
"Because I know him better now, that's one of the reasons why I kept him in the team.
"He acknowledged that he missed his game and he will respond because he has the strength to do it.
"I am not happy only because he scored a goal, but also because of the work rate he put in today from the first to the last minute."
Despite their shortcoming in Europe, Arsenal remain in good domestic form following a third successive league win
Wenger said: "We have three more points than last week and if you look at our Premier League run since November, I think we are in a good position.
"On the fluency front we can do better, but today our first worry was just to win the game."
Everton, who were impressive winners of their Europa League tie against Young Boys on Thursday night, had plenty of possession, but could not find a way past David Ospina, who made a fine point-blank save from Romelu Lukaku just after the hour.
Manager Roberto Martinez accepts his team are "not enjoying" their Premier League campaign this season with only one win from the last 11.
"You have a 2-0 scoreline, but it doesn't reflect what happened on the pitch
Unfortunately that is the story of our season," he said.
"We have not had the momentum that allows you to win games, that is something we need to change quickly."
Martinez added: "It has been more of a chore than enjoying our football
I have not seen that enjoyment in our team in the league with points at stake.
"I do see that enjoyment in the Europa League, but I feel the group is becoming stronger."
Source : PA
Source: PA