The Gunners - facing up to life without Thierry Henry - were under pressure for large spells at the AXA Stadium, before Cesc Fabregas grabbed a crucial away goal and Alexander Hleb netted again in stoppage-time.
Wenger said: "It was a very physical game. Sparta played with a total commitment in the first half and stopped us from playing.
"We needed to be patient and not make a mistake.
"At one stage we were lucky as well, because they hit the post.
"We needed to play with more purpose in going forwards and did that more in the 2nd half.
"Then we were more dangerous.
"The whole team has a resilience, they fight to the last second - and we have shown that again tonight when we scored the goal."
Wenger added: "I am very pleased with the result.
"At 2-0 we are not qualified. We know we have to keep on our toes.
"But the second goal was certainly a mental blow for them."
Wenger said: "I feel against Fulham, he made a big mistake in first minute after he had a good performance and showed mental strength.
"Today had great saves and was very influential on the second goal we scored as well."