Spaniard Costa has 17 goals in the Premier League this season but has only found the net three times in 2017 meaning he is still looking for his 50th strike in Blues colours.
But his manager has defended his out-of-form striker insisting that goals are only part of what Costa brings to his team.
Chelsea vs Manchester City player ratings
Chelsea vs Manchester City player ratings
1/22 Thibaut Courtois - 6
Completely at fault for Aguero's equaliser - a rare lapse in concentration. Showed his strengths moments later though to deny Sane a one-on-one chance on goal.
2/22 Cesar Azpilicueta - 6
Decision making was on point for much of the evening and kept a calm head under pressure.
3/22 Kurt Zouma - 7
A respectable return to the starting line-up. After months on the sideline he seemed to cope well with both the pace and intensity of the game.
4/22 David Luiz - 7
A fierce and fiery performance from the Brazilian. Hit hard in his challenges and dealt with Aguero well.
5/22 Gary Cahill - 6
Solid as ever in his reading of the game and challenges, both on the deck and in the air.
6/22 Marcos Alonso - 6
Handled his defensive duties well and proved effective on the front foot.
7/22 N'Golo Kante - 6
Industrious as ever with his running and positioning but one of his more quiet evenings. Conceded a sloppy foul on the edge of his own box which City nearly equalised from.
8/22 Cesc Fabregas - 6
Kept the ball moving well in the middle and was relatively effective in dictating the flow of the game.
9/22 Pedro - 7
Dealt well with his defensive responsibilities tonight and got well forward to put the City defence under pressure. Questionable touches/passes here and there but overall a good night from him.
10/22 Eden Hazard - 8
Once again, Hazard proved to be the difference. Took his first goal well from a difficult angle and reacted well in his penalty attempt to grab Chelsea's second.
11/22 Diego Costa - 6
Another mixed performance. Menaced the City backline with his physical presence but his hold-up play was found wanting at times. It ultimately fell to others to make the difference tonight.
12/22 Willy Caballero - 6
Completely misjudged Hazard’s first goal. Despite taking an unfortunate deflection off Kompany, he should have done better in dealing with the strike. To his credit, he saved Hazard’s initial penalty kick but couldn’t stop the forward from following up.
13/22 Fernandinho - 5
His reckless challenge on Pedro cost City dearly and handed the home side their second goal. Too hot-headed.
14/22 John Stones - 6
Dominated in his aerial battles but struggled to deal with Hazard’s pace and quick feet. Had a glorious chance to equalise in the second half but couldn’t find the goal.
15/22 Vincent Kompany - 5
For all his fight and heart, there was a certain sharpness missing to his game tonight. His weak positioning afforded Hazard the space for his first goal while his lack of pace saw him struggle to keep up with the tempo of the game at times.
16/22 Gael Clichy - 6
Linked up with City's forward players well and was a nuisance in getting in behind the Blues defence.
17/22 Fabian Delph - 5
A series of early, well-timed challenges boded well but he looked out of depth at times. Not a surprise given his lack of Premier League football this season.
18/22 Jesus Navas - 5
A quiet evening as a whole. Had very little say for himself.
19/22 Kevin de Bruyne - 6
Sloppy passing in the centre of park let team-mates down on occasion. Kept him self busy nonetheless and wasn’t afraid to take on his opposite men.
20/22 David Silva - 7
One of City’s more effective players - especially in the first half. His slick passing and clever link-up play kept the visitors’ midfield ticking over. Created numerous chances too and found himself well positioned to set up City’s equaliser. Couldn't find that all important equaliser though.
21/22 Leroy Sane - 6
Had the chance to put City ahead after Aguero’s equaliser in the first half. Flashed with brilliance but couldn't sustain such form throughout the night.
22/22 Sergio Aguero - 6
A classic poachers finish for City's goal. Certainly kept the Chelsea backline busy but it wasn't to be his night.
"Goals are very important for the forwards," Conte said. "But I think he knows that, for us, he's an important player if he is scoring or if he doesn't score.
"He must continue with his commitment and then I'm sure he'll score. He's playing good football and doing what I want. I'm not concerned about this.
"I speak with all my players if I'm not happy with someone's commitment or behaviour, but not if he's not scoring.
"It can happen. In a lot of circumstances he was unlucky. But a player like Diego Costa can score in every game and I'm sure he can do this."
Costa won LaLiga in Spain with Atletico Madrid in 2013-14 before claiming a first Premier League title with Chelsea a year later after a £32million move to Stamford Bridge.
Now in his third season at Chelsea, Costa is seeking a second Premier League triumph, with the Blues seven points clear of second-placed Tottenham ahead of Saturday's match at Bournemouth.
Throughout his time with the Blues he has been linked with a move away - a return to Atletico is perennially raised - and in January there were suggestions of a bust-up with Conte over the possibility of a move to the Chinese Super League which did not materialise.
Conte lauded Costa's character.
He said: "The quality is his experience. His character. His personality. That's very important for us and the team. Also, Diego won in the past and he has good experience."Reuse content