Saturday's 1-0 loss to Southampton at the bottom of the Premier League standings increased the pressure on Chelsea manager Graham Potter.
In the second half, Azpilicueta required nearly 10 minutes of treatment on the field after receiving a kick to the head during a goalmouth collision.
Physiotherapists from both teams came to his help, and he was ultimately taken out on a stretcher.
With the substitutions of Raheem Sterling and Kai Havertz, Chelsea were more spirited in the second half and put the Southampton defence under pressure.
In the last seconds of extra time, Southampton goalkeeper Gavin Bazunu made a fingertip save against replacement Conor Gallagher.
Chelsea are now in 10th place with 31 points after 23 games, 10 points behind the top four.
Potter left Brighton in September to replace Thomas Tuchel at Chelsea, but has unable to improve the club's fortunes despite spending significantly on transfers in January.
"Our season has been difficult," Ward-Prowse told the BBC. In all parts of our game, we have lacked consistency.