Cesc Fabregas scored on his 300th Premier League appearance, but Fernando Llorente equalised on the stroke of half-time against the run of play.
Pedro scored Chelsea's second when his shot deceived Swansea's goalkeeper Lukasz Fabianski and Diego Costa added a late third as Conte's men won a 12th successive home game.
"It's right for me to help them to be focused in every moment," the Chelsea head coach said.
"We played first half really well and it was a pity to concede the goal at the end of the first half.
"Maybe the time was finished, but in this case you must pay attention.
"I told them, 'We are playing very well, we are dominating the game, we created some chances, but we stay 1-1
We don't deserve this, but the reality is now we are 1-1
For this reason go in the second half and push, because we need to win'
They did this.
"I think it was very important because in this situation when the tension starts to increase, it's important also to see the right answer from my players.
"And today I saw a lot of right answers from my players."
Second-placed Manchester City are not in action this weekend, but Tottenham could cut the deficit to 10 points with victory over Stoke on Sunday.
Chelsea's lead is commanding with 12 games to go, but Conte is taking nothing for granted and believes his squad has plenty of title-winning experience to fall back on in the run-in.
He added: "To keep the concentration for the whole championship is not easy.
"But I have a lot of players that played and won in the past
They know very well the way that we must continue to try to keep the top of the table, to try to win the title.
"For this reason I'm lucky
I'm lucky to have a lot of players that in the past won a lot.
"We are deserving to stay on top of the table, because we are playing good football, with good intensity.
"I'm very happy, above all for my players."
Fabregas was selected ahead of Nemanja Matic for his first Premier League start of 2017 in the sole change to the starting XI from Chelsea's 1-1 draw at Burnley in their previous Premier League game.
Conte is pleased to have selection dilemmas and cited another in choosing between Willian and Pedro.
Pedro started again and scored for a third straight game.
"Pedro is showing his quality," Conte added.
"The formation is exploiting his characteristics."
Swansea's only defeats in six league games under former Chelsea assistant boss Paul Clement have come to Arsenal, City and now the Blues.
And the visitors felt aggrieved at being denied a second-half penalty when, with the score 1-1, the ball appeared to hit the arm of Cesar Azpilicueta.
Referee Neil Swarbrick dismissed the appeals and Clement did not approach him about the decision afterwards.
Clement said: "I thought it was a penalty
That should've been given.
"I've seen it again on the video and I think he (Swarbrick) had a good view of it."
On Pedro's goal, with a shot which went beneath the Swansea goalkeeper, Clement added: "Fabianski is disappointed
You could see from his reaction.
"You never want to lose a game, but the performance doesn't damage our confidence.
"We've had some really difficult away games, and picked up some good home results
The month of March is vital."
Swansea play Burnley, Hull, Bournemouth and Middlesbrough in the next few weeks and Llorente will be key in their survival fight.
The Spain striker was linked with a move to Chelsea in January and showed why.
"I wasn't always confident we'd keep him, but I'm certainly glad we have," Clement added.
"He's a key player for us, and will be a big help for us in the run-in."
Source : PA
Source: PA