Despite Milan's dominance of possession, Heurelho Gomes only made three saves in the 90 minutes and the biggest scare arrived early as William Gallas cleared Robinho's effort off the line in the first half.
"It was backs to the wall for 90 minutes but we stood strong," Dawson told the Spurs website. "What a night out there. The atmosphere was incredible.
"It was a tough night for us, not just myself and William Gallas, but the whole team. We had to defend for our lives and we did that.
"The game plan wasn't to go out there and defend but you have to give credit to AC Milan. We couldn't get out like we wanted to but we showed a different side to our game, everyone defending and getting behind the ball. We made it hard for them.
"Everyone in front of the defence made our jobs a lot easier - Sandro, Luka, Steve, Azza, JJ when he came on. It's not about individuals out there, it's a team game.
"AC Milan are a top team and we've showed over the two legs that we can mix it with the best.
"Hopefully we'll keep it going for as long as possible and we'll have more nights like this."