Spurs beat Arsenal on March 3 to move into third place and open up a seven-point gap between their rivals - but a return of four points from their following four Premier League games has handed the Gunners the chance to overtake Andre Villas-Boas' side.
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And when asked if the mood is affecting the players, Dempsey told reporters: "I don’t know. It’s something that’s been there. It’s been noticeable in the last three home games.
"It’s been tense. I’ve felt like that’s kind of what the atmosphere’s been. That’s the way it’s been the last few games.
"You’ve got to keep going. You’ve got to do everything you can to help the team win. You can only try your best. It’s going to be a fight all the way until the end."
The United States international is unsure as to why Tottenham's form has dipped in recent weeks but suggested it could be down to injuries and a congested fixture schedule.
Star man Gareth Bale missed the 2-2 draw with Everton through injury but the club are hopeful of a return against Manchester City on April 21 - although Spurs will also have to navigate their Europa League quarter-final second leg against Basel in the meantime.
He continued: "Who’s to say the reason why? Maybe a few injuries, maybe a lot of games. It makes it more interesting for people to watch. It’s a little bit more stressful but it’s a good stress. At least we’re pushing to try to get that [Champions League] spot. Hopefully we have enough character to get the job done.
"I thought the boys showed a lot of character to fight back and get a point against Everton. It’s an important point. You would have like to have got three but at least we fought back. We have the quality. It’s about being confident. It will be difficult all the way until the end of the season."