Stoke twice drew level at Stamford Bridge, but Willian scored his second and Diego Costa Chelsea's fourth as Conte's men emulated Arsenal's 2001-02 feat of 13 straight wins in a single season.
"After the second goal it wasn't easy to go and have the good reaction, to show the great character, above all after 12 wins in a row," Conte said.
"When you win a lot there is a great danger to be satisfied, to be relaxed, to think 'okay, but we won a lot in the past, now if arrive the draw, if we don't lose, if we don't win it's not important'
No.
"My players showed me great will, great will to fight, great will to win, great will to take this great achievement for us
I'm pleased for them and they deserved this
I'm their coach, but they deserved this."
Arsenal extended their winning sequence by a game to 14 the following season and Chelsea can match that streak at rivals Tottenham on Wednesday.
It was the first time Chelsea had conceded more than one goal in a game since the September 24 loss to the Gunners, but the subsequent run has seen the Blues enter 2017 as the title favourites.
Conte knows the challenge will be more difficult, beginning at White Hart Lane.
Conte added: "Now it's not easy after 13 wins in a row you face teams that want to beat you not only to take three points, but for many reasons
It's more difficult
We must know this.
"(But) when you have these type of players you can go to sleep happy.
"This first half of season was incredible for us
I think it's very difficult to repeat this run, because we played 19 games
To win 16 games, draw one game and lose two games is a great achievement for us.
"It's important to know it's not easy to repeat this run.
"The second half of the season will be very difficult for us
We started this season as an underdog, underestimated.
"We ignite the light on Chelsea
We must know this
For this reason we must know we have to work more hard and to find game by game, to see game by game, to find the right solution in every game to try to win.
"It won't be easy, but today we are very happy."
Stoke came close to ending Chelsea's winning run.
Bruno Martins Indi and Peter Crouch - with his first Premier League goal since May 2015 - struck to cancel out goals by Gary Cahill and Willian.
But the Brazilian's second and Costa's 14th of the season secured victory.
Stoke boss Mark Hughes saw reasons to be optimistic from the performance despite his side's winless sequence being extended to five games ahead of Tuesday's clash with Watford.
Hughes said: "We came here with good intentions, trying to produce a positive performance.
"(But) against good opposition, we're getting punished for every mistake we're making
We need to defend better than we are at the moment.
"We'll take the positives
We showed real belief and character to get back into the game, but we needed to do the right things at key moments of the game
And manage it to a conclusion.
"That'll change in the new year
We're a decent side at this level
We just need to get back on track."
Having lost to Liverpool and Chelsea in recent games, Hughes was asked to appraise their respective title chances.
He rates both highly, but believes the title race could come down to the fitness of one man.
"Costa's performance today showed the value he gives to Chelsea," Hughes added.
"You wouldn't want Chelsea to lose him because that could significantly damage their ability to win the league."
Source : PA
Source: PA