Wenger admitted he would have liked his team to score a second but was happy that they managed show a gritty side to their game to hold on for a tight win.
The Frenchman told reporters: “I thought that if we scored the second goal then maybe, we could [have] given a psychological blow to Everton. We had a brilliant start and slowly Everton came back into the game after about 30 minutes, we could feel that in the last 15 minutes of the first-half.
“Second-half, for the most we did hang on, until the last 15 minutes we started to create chances again, but it was all Everton. We were resilient, focused with a great desire to defend and our defence played very well tonight.
“We refused to play a little bit because we just wanted to keep the score and credit to Everton they played very well in the second-half.
“You’ve seen a side of us that people don’t know, I think it’s good that we can do that as well, we didn’t panic, we defended well on crosses which is usually not our strong point and that’s good for us.”
Arsenal have now moved above neighbours Tottenham into third in the league after languishing in the lower reaches of the table earlier in the season but Wenger revealed he was always confident that his players could turn around that situation.
The 62-year-old said: “I was always optimistic, because if you look at our results from October onwards we had only one bad spell and we lost three games on the trot because we had no full-backs and the attitude of the team was always good, so I felt we could bounce back.
“We needed to be strong because we’re under a lot of pressure and I think we need that until the end of the season because where we come from we know what suffering means.
“That shows you that things change quickly in this league and so that’s why for us it’s vital to keep our focus."