Speaking to Sky Sports after the match, England midfielder Dier struggled to hide his dejection.
"It was already going to be hard before, so now it's even harder. That's all I can say really," he said.
"It's disappointing really because we were on a fantastic run and we didn't think it was going to stop.
"They made it hard for us, they played very deep and we couldn't create many chances."
Dier added: "We brought it [the deficit to Chelsea] back to four points but after today it's nearly impossible now.
"We'll give everything for these last three games, no matter what."
Tottenham return to Premier League action for the final game at White Hart Lane against Manchester United next Sunday, by which time Chelsea could already be champions.