Costa scored his seventh Premier League goal of the season as Chelsea beat champions Leicester 3-0 at Stamford Bridge.
The Spain striker is one yellow card away from suspension and appeared to call for his own withdrawal midway through the second half
Had he been booked he would have missed next Sunday's reunion with Jose Mourinho, when Manchester United visit.
Conte insisted it was his choice alone not to take off Costa and downplayed suggestions the striker was feeling his troublesome hamstrings.
"If I can, Costa I keep him until the end," Conte said.
"I can take the risk about this, for a yellow card or for injury
"Diego is in good shape
Costa is an important player to us.
"He has a good personality
We need his passion in every moment of the game."
Costa was given the freedom of half of Leicester's penalty area to score after seven minutes before Eden Hazard and Victor Moses completed victory, extending Leicester's miserable start to the defence of their unexpected title.
The Foxes were robust last season, but have now conceded a league-high five goals from corners this term.
Leicester boss Claudio Ranieri said: "We have to do something.
"It's not a name, it's not who's playing or not, it's the concentration
Now too many times we concede a goal from set-plays.
"The first half the performance wasn't good
We conceded two strange goals
The first corner, (he) was alone
It's not me alone (it was) Costa
It's not easy to leave him.
"The second was a ricochet
It was unbelievable what happened this season."
Leicester have eight points from eight games in a similar post-title malaise to Chelsea's of last term, but Ranieri is focused on working to respond.
"I'm not worried
I know my job," he said.
"It's difficult to say what happened this season
You see it's a different Leicester.
"Also me and my players - we see it's a different Leicester
Now it's important to understand why."
Ranieri acknowledged Leicester's first foray into the Champions League has had an impact, but still demands the same level of concentration domestically.
The Foxes play Copenhagen on Tuesday night and Ranieri rotated his options with that game in mind.
Riyad Mahrez did not start a Premier League game for the first time in a year, while Islam Slimani and Danny Simpson were also dropped to the substitutes' bench.
The Foxes boss insisted he would make the same decision again.
He added: "The Premier League is one year long
Champions League is two months, in or out.
"We want to go in the knockout in Champions League or Europa League
To achieve this you have to have all your players fit.
"And I prefer to preserve some players for Tuesday night."
Ranieri denied suggestions resting players sends out the wrong message.
"If Chelsea is not an important match, you have to close the bar or the pub," Ranieri added.
N'Golo Kante turned down Champions League football with Leicester to move to Chelsea and showed his former employers what they were missing with a fine performance.
But Ranieri downplayed the loss of the France midfielder.
"Kante wasn't in our box last season when we have the corner (to defend)," he said.
"Of course N'Golo Kante was important for us, as were all the other players.
"(But) it's not only one man that changes the team
It's the brain (mentality) that change the team."
Conte on Friday laughed off suggestions he was about to be sacked after some bookmakers suspended betting on his departure a day earlier.
And Chelsea's best performance of the season was the on-field response.
"I'm quite tranquilo
I'm very happy," said Conte, who dedicated the performance to Willian and his family after the Brazil playmaker's mother died during the week.
"When you work so hard during the week, it's logical you want to see a good result, good play, a good game.
"I saw this
I'm very happy, above all for my players."
Source : PA