The USA international scored twice against Coventry as Spurs secured a place in the fourth round and is confident the squad has enough quality to compete on all fronts
Spurs defeated Coventry 3-0 on Saturday afternoon with Dempsey netting twice as the hosts scored all three goals before half-time at White Hart Lane.
The win extended Tottenham's unbeaten run to six games in all competitions, and Dempsey believes Andre Villas-Boas' side possess enough talent to compete on all fronts.
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"We want to do well in all the competitions that we remain in and we want to finish in a position that qualifies us for the Champions League next year, and hopefully we can do that."
However, the forward was wary of predicting a challenge to Manchester City's grip on second in the Premier League, despite Spurs being just six points behind the reigning champions.
He added: "We just take it one game at a time. Our next game is QPR away, we need to make sure we continue on this good run of form, and make sure that we try to get as many points as possible from the games in front of us.
"You want to do well, you don't want to look too far ahead, you want to keep your feet on the ground and know that there's a lot of hard work you've got to put in if you want to accomplish your goals, so we're not going to get too far ahead of ourselves. Our focus is on the next game and making sure we get the right result."
Having recently recovered from a torn abductor muscle, the USA international is also looking to kick on and contribute more goals and assists.
"It's going OK," he said. "I've got six goals and five assists in all competitions now, so it's starting to look better. I'm someone who likes to score goals or get assists so it's good to be getting my stats up and contributing and trying to help this team do well.
"It's going good but I still want to do better."