He replaced Gareth Bale in the 79th minute with Spurs 3-0 up.
"It was great, especially to go away from home and dominate the game the way the lads did, to keep possession and create chances," Dempsey told the Spurs website.
"That's why I want to be here, it's a great team with plenty of quality players in the squad.
"It was good to go away with the national team, play two games and get a goal under my belt and then come back and get my first game.
"Now it's about trying to fight for more minutes and trying to make an impact."