Winless Burnley frustrated Arsenal at the Emirates Stadium for 70 minutes, before Alexis Sanchez headed the hosts in front and Calum Chambers scored his first senior goal soon after.
Sanchez added a third late on as Wenger's side recorded consecutive Premier League wins for the first time this season.
And the Frenchman was quick to praise his team's attitude after the game.
"We had strong team pressure and we had to intensify that in the second half, which we did, and slowly you could see that the chances were coming and it became easy once it was 2-0," said Wenger.
"But they did fight very hard and we didn't make mistakes at the back and overall I think it was a very satisfying win.
"Recently at home we did not get the results we wanted but for the confidence of the team as well it is important to win without conceding a goal.
"In recent games we were not patient at home and we have learned maybe, and we look a bit more balanced between offence and defence and less in trouble when we lose the ball. Today we were serious and that is very important to the efficiency."
The performance of Sanchez caught the eye as he scored his ninth and tenth goals of the season.
Sanchez appeared to offer something different for Arsenal in attack and Wenger believes this is a result of his mentality on the pitch.
Wenger added: "The header he scored is more the result of determination, of desire than of doing something special technically.
"He has the attributes of a fighter and of a quality player, a talented player. That is what you want to see in every football player.
"Since he began playing through the middle he appears more goal dangerous.
"We had about 30 crosses today and for a while we couldn't win any headers and in the end he got there. He jumped very high and got there, he is a winner."
With the result sealed, Wenger was also in a position to give Theo Walcott his first appearance since January, as the England international steps up his recovery from a serious knee injury.
Wenger said: "I could give him 12 or 13 minutes today when the game was done and you could see that his movement and his decision making was good, he needs now to get used to competition."
