The Gunners were unable to fully capitalise on their first-half superiority at the Emirates but Olivier Giroud scored just before half-time to put them into the lead.
They then weathered some West Ham pressure after the break, before Aaron Ramsey and Mathieu Flamini wrapped up the victory with second-half goals.
Wenger said: ???I think we played very well in the first half and created chances but we could not finish the chances off. Their keeper (Adrian) kept them in the game.
???We scored a great goal just before half-time but second half, coming out, West Ham put us under pressure.
???We needed to be well organised and stop them from scoring. Then, in the last 20 minutes, we were on top of the game and looked always like we could score goals.???
However, Wenger admitted that he had been anxious when the score was just 1-0.
???We know they have the quality,??? he said. ???If you look at the results of West Ham against the top teams, since the start of the season, they have done extremely well.
???They had injuries but I felt they played well. Cheikhou Kouyate at the back played well, for example, and overall they played with great spirit and great quality.???
The stylishness of Arsenal???s goals naturally pleased the manager, who added: ???It is a game we love to play.
???When we don???t score, of course it is questioned, but I think the players know each other well, they know how we want to combine, and it makes us much more efficient.???
And Wenger does not think a big upset is out of the question in France on Tuesday, although his team face a daunting task, having suffered a 3-1 defeat in the first leg at the Emirates.
???We had a good week and it puts in a good position to prepare well for Tuesday night,??? he said.
???We know we have a massive challenge but we will give absolutely everything. Another 3-0 would be an ideal result but let???s see what we can do.
???The pitch (at Monaco) has never been fantastic but we have to adapt and not look for excuses. Just go for it and give our best.
???They are favourites now but we can reverse it. We just have to make sure the spirit, desire and belief are there.???
Arsenal???s Premier League form is superb and they are now just a point behind second-placed Manchester City, who lost at Burnley on Saturday night.
“We just have to keep going,??? said Wenger. ???We have won eight of the last nine and we are stronger today than we were at the start of the season.
“We dropped off in this league because we won one of six at the start of the season. Today, we are a different team.???