Spurs are now seven points clear of the Gunners.
"It's massive to go seven points clear, in a North London derby, to get three points is massive but we have a long way to go, but it is a good day," Dawson said on Sky Sports 1HD.
"We have a great squad and we showed that today.
"It probably wasn't our best performance. We didn't keep the ball like we know we can but showed great determination and we got the three points we deserved.
"We want to be back in the Champions League. I think we showed that in the celebrations after. The fans will go home happy and have the bragging rights at work tomorrow."