"We needed spirit and we needed nerves as well," Wenger told reporters after his side had come from behind to win 3-1 at home.
"We have shown both, I think, and in the end got a win we deserved."
Arsenal rose to third in Premier League, above their London rivals Chelsea and Tottenham Hotspur, and are now well placed in the race for Champions League qualification with six games of the campaign remaining.
Their current good form, however, is in contrast to their early season displays, which put them out of contention for the title and saw them fail in successive cup competitions amid calls for Wenger to be eased out.
When they lost to fourth-tier Bradford City in the English League Cup, British media labelled the Gunners toothless and lacking the stomach for a scrap.
Yet there was plenty of heart on show as they scored three goals in the final five minutes on Saturday.
Wenger, who was accused of losing his touch as Arsenal stumbled earlier in the campaign, can also be satisfied that his substitutions had a decisive effect.
Alex Oxlade-Chamberlain, a second-half replacement for Bacary Sagna, set up Arsenal's second goal, and Lukas Podolski, who came on for Gervinho, drove in a third in added time.
"They had a good impact," Wenger said. "They came on with a good attitude and a good spirit. Once Norwich got a bit tired, they made a difference."