Theo Walcott opened the scoring against the League One outfit in Wednesday's third-round encounter, but the Gunners were made to sweat in the latter stages of the game.
Wenger told BBC Sport after the game: "Yes that was hard work, credit to Doncaster, they kept going. We started well in the first 35 minutes but we decreased slowly.
"We lost our collective game and couldn't score the second goal, it became more difficult. We wanted to score goals we were just lacking. It was a typical cup game. I was concerned, they looked dangerous."
Arsenal's reward for progress in the competition is a fourth-round tie against Norwich City, to be played in the week commencing October 23.