Olivier Giroud headed the only goal of a tight game at St James' Park on 65 minutes, as Arsenal followed up a win at West Ham on Boxing Day with another three points on their travels.
Chances were scarce for both teams and Wenger acknowledged his team retreated slightly after Giroud's goal had given his side the lead.
"We had to dig deep today," the Arsenal manager told Sky Sports.
"I think we controlled the game quite well and we restricted them to basically no chances, but they are a good team.
"There were two aspects to the game. The first was leading up to 1-0 when we were quite in control, but after that we subconsciously only wanted to defend.
"Of course, there were some situations in our box, but our spirit got us through."
Wenger also underlined the more physical qualities that Giroud brings to the side, saying: "That is what you need in a team.
"He has these qualities, that of course is very important.
"We are small and technical, so to have a player up front to counterbalance that is important."