The victory moves Spurs just three points behind second-placed Liverpool, who play Manchester United on Sunday, and Pochettino said his team must keep believing, per the Press Association (h/t BT Sport).
"We are in a very good position; we are there and that is the reality, that after 17 games and 39 points we are third. That is a massive achievement for us. We are there now but everything is possible.
"Look what happened in the Champions League: after three games only one point and we believed it was possible and in the end we believed and now are in the next stage.
"There are a lot of things you need to put into consideration but the most important thing is belief and faith in the way you work and if you give 100 per cent all can happen."
Spurs left it late to claim all three points at Wembley Stadium. Substitute Christian Eriksen scored the winner in stoppage time to make it 17 matches without a draw for the north Londoners:
The result caps a fine week for Spurs, who booked their place in the knockout stages of the UEFA Champions League with a 1-1 draw against Barcelona at the Camp Nou on Tuesday.
Tottenham had looked unlikely to qualify after taking just one point from their opening three fixtures against Inter Milan, Barcelona and PSV Eindhoven. However, they managed to turn their situation around and will be part of Monday's draw for the last 16.
Saturday's victory also saw Pochettino hit a landmark with Spurs:
Pochettino's men have now won 10 of their last 12 Premier League games and are just five points behind leaders Manchester City.
Manchester City and Liverpool remain big favourites to land the title this season, but Tottenham's fine form has propelled them into contention and means they can not be discounted just yet.