The Gunners struggled to break down a resolute visiting side until Bendtner's 89th- minute strike, before Theo Walcott wrapped up the win moments later.
Wenger believes the changes he made in the second half gave Arsenal an added attacking impetus when it was most needed.
In the second half we upped the tempo and won in a deserved way but Cardiff worked very, very hardArsène Wenger
"Credit to the players who came on, they gave us freshness going forward," Wenger told Arsenal Player. "They had a good impact so it was a great relief and you could see that everybody was hugely happy.
"I don't deny that the first half was a bit slow, we found it difficult to get going again but we didn't make a mistake at the back.
"In the second half we upped the tempo and won in a deserved way but Cardiff worked very, very hard."
Wenger was left with mixed emotions after Bendtner picked up an ankle injury in the aftermath of his goal.
"I'm sad because he scored his goal and at the moment he needs this kind of goal to get credit again," he said "Unfortunately he got injured so I'm really sad for that because we lose a striker of quality.
"He has quality, who questions his quality? Nobody. What you want from him is to be focused on giving absolutely 100 per cent and he is a great centre forward."Copyright 2014 The Arsenal Football Club plc. Permission to use quotations from this article is granted subject to appropriate credit being given to www.arsenal.com as the source 2 Jan 2014