The situation meant United became the first Premier League team to make three substitutions in the first half since Burnley had to do it in January 2015, in a game against Newcastle United.
Herrera was the first player to depart after 20 minutes, as he went down holding his hamstring. The Spaniard was replaced by Andreas Pereira.
Mata followed his compatriot back to the dressing room five minutes later after he was injured in a challenge from James Milner. United's no.8 had initially hobbled on and he successfully denied Mo Salah a goalscoring chance, but he was then replaced by Lingard.