Emerson lasted only 15 minutes at Stamford Bridge, with the left-back suffering a muscle injury and limping off straight down the tunnel, with Marcos Alonso replacing him.
As the first half wound down Christensen also had to go off when the Dane was caught by his team-mate Fikayo Tomori, who was sliding to block a shot from Mohamed Salah.
Kurt Zouma was introduced in Christensen's place, with Chelsea down 2-0 after goals from Trent Alexander-Arnold and Roberto Firmino.
That advantage would be enough for the visitors, as Chelsea fell 2-1 despite a stunning second-half goal from N'Golo Kante.
Should the defensive duo be forced to miss time it would be a blow for Chelsea, with both players having established themselves as starters under new manager Frank Lampard.
Christensen, who struggled for minutes under Maurizio Sarri, has started five of Chelsea's six Premier League matches thus far.
Emerson, meanwhile, has overtaken Alonso on the depth chart and has also made five Premier League starts in the 2019-20 campaign.
Christensen and Emerson would be added to a growing injury list, with the Blues already missing a number of key players.
After being out with a knee problem, normal defensive starter Antonio Rudiger made his first appearance of the season against Wolves last weekend, but had to be removed at half-time with a groin injury,
Rudiger missed out on Chelsea's loss to Valencia in midweek as well as Sunday's game against Liverpool.
Meanwhile, right-back Reece James has yet to make a first-team appearance with Chelsea this season but stepped up his injury recovery on Saturday when he played for Chelsea's Under-23 team.
Also participating in that game was Callum Hudson-Odoi, who is recovering from a torn Achilles tendon suffered in April.
Chelsea will be hoping to welcome back James, Hudson-Odoi and Ruben Loftus-Cheek – who is recovering from the same injury as his fellow England international – to the first-team picture in the coming weeks.