The 29-year-old Dempsey was paired in the attack with Jermain Defoe by manager Andre Villas-Boas against Manchester United on Sunday and rewarded his boss when he scored a 93rd-minute equalizer to force a 1-1 draw with the league-leading Red Devils.
Adebayor is certain to miss Spurs' next two games at least, and Dempsey, who has scored seven goals so far this season, sees it as the perfect opportunity to prove his worth.
"Ade is a great player and he is going to be missed, but there is competition," Dempsey told reporters. "You try and fight for a spot and when you get an opportunity to play you want to stand up and take advantage of that opportunity.
"I can play that position [striker]. It's a position I feel comfortable in, a position I have played a lot this season and I feel like I am starting to feel more comfortable there.
"Now it's about just trying to create more chances in the attacking third, whether it's getting goals or getting assists, and I feel like I have been on a good run of form."
Dempsey overcame a slow start to the season has come on as of late, scoring five goals in his last seven matches.
"For me, it was a slow start to the season, so it's good to be chipping in with goals now and repaying the club for their belief in me," Dempsey said. "Hopefully there will be more goals to come because that's why they brought me here."
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