Alex Song's late header denied struggling West Ham a share of the spoils at Emirates Stadium and kept the Gunners five points behind leaders Chelsea.
It was, though, far from a vintage Arsenal performance as time and again the home side were left frustrated by some fine goalkeeping from Robert Green, who impressed in front of the watching England coach Franco Baldini.
The Gunners also failed to make the most of decent build-up, while Samir Nasri's long-range free-kick hit the crossbar before substitute Theo Walcott struck the base of a post.
Wenger, however, feels his young side again showed their maturity by not letting the tempo drop, which was eventually rewarded when Song headed in Gael Clichy's cross with just two minutes left.
"It was a battle where we needed to be patient and intelligent, to keep our game structured, which we did well," Wenger said. "We were unlucky on a few occasions and West Ham defended really well – their 'keeper had a great game against us as usual."
For West Ham, it was another hard luck story which has plagued their season.
However, manager Avram Grant remains ever the optimist, and believes with matches against Birmingham, West Brom and Blackpool coming up, there is no reason to think the Irons cannot start to climb the table.