The Gunners were made to wait to open the scoring after some resolute Norwich defending, but a stunning volley from Aaron Ramsey broke the deadlock in the 53rd minute before Carl Jenkinson made sure of the victory.
The result consolidated Arsenal's grip on the final Champions League place for a successive season, with the focus now turning to the prospect of silverware as they face Hull in the FA Cup final.
With their Premier League duties now over, Wenger admits the match provided an important opportunity for some returning players coming back from injury.
He said: "I am pleased because we got the clean sheet, 17 in the season and 11 away wins in the league is the best we have had and we have been consistent.
"We wanted to give competition to players who have been out for a long, long time but what is important is that these players are back.
"It is important moment of the season and we want to prepare to be ready for a top performance in the FA Cup."
Wenger was keen to praise one of the players who will be competing for a starting berth in the final, Aaron Ramsey, who scored the Gunner's spectacular opener.
He said: "It was a fantastic goal, he has that instinct in the confidence and made the right decision and he is spontaneous you feel it's natural."