"We are not where we want to be and it is important we respond quickly, and that is down to the next game," the Frenchman told Sky Sports News.
"Overall, it is a game we have come out of very disappointed because we feel we should not have lost it."
Wenger also questioned the officials after van der Vaart's opener could have been ruled out for handball, before the Dutchman celebrated in the Spurs crowd, an offence which should have earned him a second yellow card.
"We lost a game when we were on top," he added. "We conceded two poor goals. I think the first goal was handball and second yellow card.
"The referee, maybe, cannot see it, but how can the linesman not see it?"
The defeat has left the Gunners in 15th place in the Premier League table, while their local rivals have moved into sixth.