The Spurs centre-back believes his side can complete the double over Sir Alex Ferguson's men at White Hart Lane on Sunday and go on to qualify for the Champions League this season
Spurs finished fourth in the Premier League last season but were denied entry into Europe's top club competition after Chelsea won the trophy to gain automatic entry, with Uefa laws stating only four teams from one country can qualify.
However, Dawson is confident his side can complete the double over Sir Alex Ferguson's league leaders, having won 3-2 at Old Trafford earlier in the season, to continue their push for a place in the top four.
"Winning up at Old Trafford was a great win for us," he told reporters. "I'm sure that will be in their minds when they come to White Hart Lane.
"It was great after so many years to beat United, but the biggest thing was to back that result up. We've managed to do that.
"It was unbelievable last season. To finish fourth and not qualify for the Champions League was devastating.
"There are a lot of teams fighting for the top four this season. We have to make sure we are because Champions League football is where we want to be. We've shown we can do it, but we have to prove it now."
Dawson also revealed that manager Andre Villas-Boas won his respect after the boss made him his fifth-choice centre back at the beginning of the season.
"The boss has got five top centre-halves at the club and he can only play two. He was honest and said he couldn't guarantee me games - I respected him for that.
"At the start of the season when I wasn't involved at Newcastle, he spoke to me. Since then I have respected his decision; there's no point moaning about it. Everyone's got opinions and, hopefully, I've changed his opinion now."
Dawson explained that Tottenham's acceptance of an offer for him from QPR could have dented his confidence, but is happy to have rejected the approach and won his place back in the starting XI.
"It was maybe difficult for me that the club accepted an offer but I chose to stay. If I had wanted to leave, then I could have done.
"When your chance comes, you've got to take it. It's great to be back playing. I've been at Tottenham for eight years and it's not always been easy.
"It wasn't the first time for me to be out and, hopefully, I've got my way back in and I can stay in the team as long as possible."