Saturday's win was only Arsenal's second in the league since the turn of the year but one Wenger believes his side deserved.
"They made it difficult for us," he said. "They were organised, defended very deep.
"We didn't find the space but we kept going and, while we are a bit lucky with the goal, we deserved this win.
"We had chances, their 'keeper made a lot of saves. We played in their half a lot and overall I think we deserved to win the game."