The festive results have meant that, if the Gunners beat Bolton Wanderers next Wednesday, they will move up to second in the Premier League table, only one point behind leaders Chelsea.
Wenger said after the rout of Pompey: "I believe it was a big game for us because we played a big game on Sunday and sometimes, three days later, you can be less focused.
"But we were committed, focused, and ready for it and played like a real team against a Portsmouth side who fought very hard.
"We were a bit lucky on the first goal but after that we controlled the game. I'm proud of the team because the belief is there and we played like a real team. It was a big game for us tonight. We knew, to keep chasing, it was important to win here.
"Tonight we showed a physical response in the first half when they made it very physical. In midfield we were really up for it and dominated physically.
"I'm not surprised at what we've done since Chelsea, when we lost 3-0. I think people at that time didn't believe what I said. It's good. It shows that not only I can be wrong, but you can all be wrong, too."
Source: DSG
