Dempsey scored twice on Thursday in Basel, 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 on Thursday, 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."
As Villas-Boas acknowledged in February, failure to qualify for the Champions League could have serious consequences for Spurs.
Tottenham's new year financial results showed a 12 per cent drop in revenue, but the biggest problem caused by another year of failure could be the potential loss of star man Gareth Bale.
A 10-day break until their next game against Manchester City - when Villas-Boas expects Bale, Aaron Lennon and Jermain Defoe to be fit again - will work in Tottenham's favour, but Dempsey has warned his team-mates they still must work extremely hard to make the top four.
"The break will help, because the more players you have fit, the more competition there is for spots," he added.
"You need that push towards the end because it's going to be difficult.
"We've got some difficult games. We've got Chelsea, we've got Man City, so we're going to need everyone fit and fighting to try to push for that Champions League.
"It's not going to be given to you. You have to fight until the end and we're still in with a shout to make that happen.
"I think it's going to come down to the last game."
The way Tottenham coped with the immense pressure on them last night bodes well for them for the rest of the season.
Amid a hostile atmosphere caused by the raucous home crowd at St Jakob-Park, Spurs looked comfortable on the ball and Dempsey gave them a first-half lead when he beat Yann Sommer after Jan Vertonghen had sliced open the Basle defence.
A mistake by Mousa Dembele allowed Mohamed Salah to equalise and Aleksandr Dragovic put Basle ahead before Dempsey struck again eight minutes from time to send the game in to extra time with the tie locked at 4-4 on aggregate.
Vertonghen's red card meant Tottenham had to play the whole of extra time with 10 men on a boggy pitch which had been hammered by rain, and Dempsey was extremely proud of his team-mates' efforts.
"We gave everything we could," the 30-year-old said.
"The boys were dead when it came to penalties. We came up a little bit short. We were a little bit unlucky.
"Everyone's upset with the result but we'll have to regroup and focus on the league."