Pochettino said his players need to believe there was still hope.
"The most important thing is the performance we showed was perfect," the Argentine told British media. "It is a big signal we are there waiting and fighting.
"We need to believe that is possible. It is good for the competition that we are in behind to try and put pressure on Leicester. I feel very proud.
"In football all can happen and, if Leicester fail, we need to be there. We need to try and reduce the gap. This is our dream."
Spurs host 14th-placed West Bromwich Albion at White Hart Lane on Monday, while Leicester take on 15th-placed Swansea City at the King Power Stadium a day earlier.
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Sudipto Ganguly)
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