Emmanuel Adebayor struck the only goal of the game as the Gunners missed chances to make it a comfortable three points.
The Frenchman told Sky Sports: "It became nervy because we did not score a second goal. Wigan defended very well and played well. They are a top quality team.
"I think the fact that we lost our last home league game meant we played a little bit with the handbrake on.
"I must praise the team because we had great focus and great discipline for 90 minutes. We had a few chances but I am happy that we can win 1-0.
"We knew a mistake could cost us three points. My players want to do well and the fluidity should come back after a home win."
When asked if he feels his charges can mount a serious battle in the title race, Wenger replied: "If I didn't believe that I wouldn't be standing here."
Substitute Emmanuel Eboue came in for strong criticism in the second period after misplacing passes and was replaced late on to cheering from supporters.
Of the incident, Wenger said: "Yes I felt it (the criticism) was very unfair because he finished the game very tired and gave absolutely everything.
"Not only was he tired, he lost his confidence and that becomes a danger so the best thing was to try and win the game and get him off."