The Brazil international was making his first start of the Premier League season, having come on as a substitute in the previous wins over Norwich City and Burnley.
However, Firmino's outing was cut short after he reported concerns over a hamstring issue to the Liverpool bench, leading to the forward being substituted in the 43rd minute.
Asked about the severity of the injury after the game, manager Jurgen Klopp said: “Serious? I don't know. Serious enough to take him off, yes.
"Bobby felt his hamstring, came and told us so we had to prepare the change. Bobby is nobody who raises the hand when he doesn't feel anything.
"It doesn't look too serious but you never know before you have a scan, which will happen tomorrow."
Firmino had 27 total touches and completed 94.1 per cent of his attempted passes during his time on the pitch, though Liverpool trailed 1-0 when he was replaced.
A Mohamed Salah penalty in first-half stoppage-time levelled the score after Reece James had been shown a red card for handling the ball on the line, preventing Sadio Mane's close-range attempt from going in.
While the Reds were unable to make their numerical advantage tell after the break, Klopp was able to see plenty of positives from the display – including another impressive outing from teenager Harvey Elliott.
The 18-year-old kept his place after making a first league start for Liverpool a week earlier against Burnley.
He justified the faith shown in him too, making more successful passes than any other home player as he continued a promising link-up with Trent Alexander-Arnold and goalscorer Salah down his team's right flank.
"He looked good last week obviously in the game, was good during the training week," Klopp said of Elliott, who became the third youngest Liverpool player ever to start against Chelsea, after John McLaughlin in 1970 and Raheem Sterling in 2012.
"We wanted to change a little bit. We wanted to have the dynamic of Hendo [Jordan Henderson] in the team, wanted to have Robbo [Andy Rovertson], wanted to have Bobby [Firmino] in between the lines.
"That all worked out pretty well and then on the right side we didn't want to change on top of that something.
"Harvey was from the first day of pre-season with us, pretty much the only midfielder we played so far [who that applies to] apart from Naby (Keita) and Ox (Alex Oxlade-Chamberlain).
"He looks fit obviously and can just deal with 95 minutes and that's important for us. It was important today and that is why we started him and that's why we left him on the pitch."
Liverpool is next in action on 13 September, travelling to Elland Road to take on Leeds United three days before opening its UEFA Champions League campaign at home to AC Milan.