After deciding to push for a move away from Fulham last summer, Dempsey saw transfer dealings drag on for longer than he would have liked.
He was unable to take in a proper pre-season as a result, with a switch to Spurs being pushed through on deadline day.
Dempsey admits that it has taken him a while to get going at White Hart Lane, but a late leveller against Manchester United on Sunday means he has now netted home and away against the Red Devils this season and has found the target four times in his last four outings.
"It's a goal that I needed," he told Sky Sports News HD.
"I had a bit of a slow start to the season, so it is good to be repaying the club back for their faith in me. They brought me in to score goals and I have been able to start chipping in with them. Hopefully I can continue as the season goes on.
"Before this season I never really scored against Man United, so to get two goals against them is great.
"I feel more comfortable with the team. It was difficult for me not having a pre-season with the team. I had a bit of a slow start, but now I feel comfortable and I feel confident."