With north London club Spurs beating Burnley, it meant the Blues’ 10-point advantage at the top of the table was cut to seven points.
And that gap could narrow even further on Wednesday, when Chelsea are at home to Manchester City on the same night as Spurs manager Pochettino's side are in action in south Wales.
"That’s a good lesson for all —- belief is the most important thing in football —- not only quality, running or being strong," said Pochettino.
"Belief, faith and fight. Nothing is impossible in football and that is our idea, our philosophy."
The Argentinian added: "We need to keep going in that direction and it’s true the Premier League is tough to play in, and to win every game and compete. It’s so competitive.
"But if it can happen? Yes, of course it can happen and our mind must be positive to try to imagine and dream and believe and give our best.
"If we are focused only on the next game and nothing around and nothing after, and if we are positive, I think we can get the three points but first of all we need to play, we need to be better than Swansea and it’s sure we will need to fight a lot against them."
- 'Massive difference' -
Spurs, bidding to be crowned champions of England for the first time since they completed the 'Double' in 1961, when they also lifted the FA Cup are in fine form.
They've won five successive games, but Pochettino insists it would take a dramatic shift in fortune to deny Chelsea the title.
"We reduced the gap by three points but it’s still a big gap, seven is a massive difference,” the former Southampton manager said.
"Chelsea, two-and-a-half years ago they won the Premier League and 80 percent of the players have experience of how to manage the pressure.
“They can win or lose but it’s not putting pressure or stress on them."
The Tottenham manager was dealt a blow ahead of the Swansea clash when young midfielder Harry Winks was ruled out for the season with an ankle injury.
Swansea, having enjoyed an initial boost following the appointment of Paul Clement as manager, are in need of a fresh lift after three games without a win.
The Welsh side's failure to beat second-bottom Middlesbrough at home last weekend was a particular disappointment and left the club one place and one point above the bottom three.
But Swansea centre-back Alfie Mawson insisted a goalless draw with Middlesbrough had not dented the squad's self-belief.
"We go again on Wednesday against Tottenham and with a big crowd behind us hopefully we can get the result we want,” he said.
"Confidence is still very high going into Wednesday’s game. The squad is fit and ready for the challenge.
"The belief is fully there that we will stay up. I am very confident in us."
Clement hopes to welcome back striker Fernando Llorente who missed the Boro game with an ankle injury.
The manager said: “We missed Fernando –- he is a big focal point for us. He has an ankle issue that I am hoping will not keep him out for long.
"Wednesday is achievable, although he is still a doubt for that game.
“He has a chance, but we are very much looking at him day to day.”