The single point leaves Liverpool third in the table on 75 points, one behind defending champions Manchester City, who have two games in hand.
The 19-year-old had only just come on as a substitute when he collided with team-mate Edson Alvarez at the London Stadium during an eventual 2-0 defeat by capital rivals Fulham.
A Ben White own goal put the home side in front before strikes from Mohammed Kudus and Jarrod Bowen early in the second period put the tie beyond doubt.
Arsenal have signed England international Declan Rice on a long-term contract from West Ham United, the north London club said on Saturday.
Liverpool boss Jurgen Klopp said on Tuesday he has taken pleasure in West Ham's revival under David Moyes as it prevented him from becoming the oldest manager in the Premier League.
The draw meant Chelsea have now won only one of their last seven league games - and they have not won away since October. They stayed ninth in the table, nine points behind fourth-placed Newcastle who have played a game less.
Chelsea are looking to win their first away game in the league since October, a run of six matches which included three losses at Potter's former club Brighton & Hove Albion, Newcastle United and Fulham.
West Ham have appoint former Everton and Manchester United boss David Moyes as their new manager.
Premier League strugglers West Ham United come back from two goals down to beat Tottenham Hotspur 3-2 at Wembley Stadium.
West Ham United manager Slaven Bilic has called on his players to drop their egos and work as one in order to end their woeful run of five consecutive Premier League defeats when they host relegation-threatened Swansea City on Saturday.
Marseille's star recruit Dimitri Payet made his debut on Tuesday but it was Brazilian Doria who booked the team's French Cup quarterfinal berth with a 2-1 extra time win over Lyon.
After selling Dimitri Payet to Olympique de Marseille for 25 million pounds ($31.2 million), West Ham United are offering fans a cut-price deal to get the French forward off their backs as well.
Olympique de Marseille have signed France forward Dimitri Payet on a 4-1/2 year contract from West Ham United after they agreed a transfer fee of 25 million pounds ($31.49 million) on Sunday.
French international Dimitri Payet's refusal to play for West Ham has led to his car being vandalised according to English tabloid 'The Daily Mail' on Friday.
West Ham United midfielder Dimitri Payet has been granted extra time off to help the Frenchman recapture the scintillating form he displayed last season and to help cope with the Premier League's demanding festive schedule.
Manchester United's Jose Mourinho is fond of setting landmarks as a manager but becoming the first individual to be sent off twice in this season's Premier League is not one he will covet.
Bournemouth forward Jordon Ibe was robbed at knifepoint when thieves rammed his car just four days after suspected gunmen allegedly threatened West Ham striker Andy Carroll.
West Ham United are determined to keep hold of Dimitri Payet, co-chairman David Sullivan has said, after media reports suggested several clubs across Europe have registered an interest in the French midfielder.
Juventas striker Simone Zaza has joined Premier League side West Ham United on a season-long loan.