Rose's sensational opener hauled Spurs to within one point of fourth place Manchester City, catapulting them back into Champions League contention.
"We needed to win to put a bit of pressure on Man City. They have got a hard game at the weekend (Manchester United) and so have we," said Rose.
"I know a lot of people wrote us off with the hard games we had coming up so it was important to get three points against Arsenal. We put in a good performance as well.
"It proves we can beat Chelsea. We have come on leaps and bounds this season. We have been more consistent away from home as well.
"It's the first time we have beaten Arsenal in 11 years and we have shown we can beat anyone at home."
"The atmosphere in the dressing room was unbelievable after the game," said Rose.
"Everyone was buzzing and jumping on Gomes. He made three terrific, world-class saves and everyone was buzzing."