Dempsey scored what proved to be the winning goal as Spurs won at Old Trafford for the first time in the Premier League era.
The 29-year-old's goal came in between a United brace, with all three being scored in less than three minutes, and Dempsey believes that his side showed good character in hanging on to the lead.
"It was a roller coaster, up and down. We found ourselves 2-0 up and then in the second half it seemed we were chasing shadows," said the American.
"But we showed a lot of resolve and got the points. I'm delighted to score because as the games go on without scoring the pressure mounts.
"It's awesome. I've been in England five and a half years and this is my first time getting three points here."
The win is Tottenham's third on the bounce as they move up to fifth in the Premier League table.