The Gunners walked away from Selhurst Park on Thursday night with all three points.
But Tomkins' late goal put the north London club on edge, and the Eagles stopper believes they showed great determination against one of the top clubs in the Premier League.
"In the first half we were majorly disappointing, they dominated and then we gave them a good game in the end," said Tomkins.
"A lot of the lads were tired out there and they moved the ball well, but we could have nicked a draw in the second half. We took the game to them and got the ball to Christian Benteke.
"The fans were pretty happy leaving, there are positives to take from the game."