Dempsey scored twice last night in Basle, but it was not enough to send Spurs through to the semi-finals of Europe's second-tier competition as Andre Villas-Boas' men suffered a dramatic defeat on penalties.
While the 4-1 shootout loss - which came after missed spot-kicks from Tom Huddlestone and Emmanuel Adebayor - is disappointing for Villas-Boas, who has staked so much on winning the competition, it does give Spurs a chance to focus all their efforts on their attempt to qualify for the Champions League.
For despite all their heroics last night, it is plain to see that, on current form, Spurs look set to fail to qualify for the biggest club competition in Europe once again.
Tottenham will drop to fifth if Arsenal win their game in hand against Norwich tomorrow, and, given that they held a seven-point advantage over their rivals last month, Dempsey thinks the team have no excuses if they fail to reach the objective that was asked of them when Villas-Boas arrived at the club last summer.
"We're frustrated we're not in this competition any more, but we have to regroup and we have to focus on the league," the United States forward said.
"We have to make sure we finish in fourth place and make sure we're in the Champions League next year.
"That's the only thing we can do to salvage this season and say we had a good year. That's been the goal for the season.
"It's important that we get into the Champions League."