It ended a 23 year drought for Spurs at Old Trafford.
"I've been in England five-and-a-half years and it's my first time getting a result here (at Old Trafford) as well, and my first time scoring against them," Dempsey told the Spur website.
"It was a great time to open my account and the importance of the game made it even more special.
"I thought we played some great football in the first half, created some good chances and got a result by scoring two goals.
"In the second half United were a different team. It was difficult for us. We did a lot of running and when you are doing that, it makes it even more difficult to try to keep possession.
"At the end, I was back on the bench and I was just praying, hoping we could see it out. The boys worked hard, blocked shots and showed great character. I think we deserved the win."