Herrera had to be taken off with an apparent hamstring injury after he went down less than 20 minutes into the game, with Mata following shortly afterwards with an ankle problem and being replaced by Lingard.
But things got worse for Ole Gunnar Solskjaer's team before the end of the half as Lingard had to go off just before half-time as it appeared he had been rushed back from injury, allowing Alexis Sanchez to step in.
It is the first time a Premier League team have had to make all of their substitutions before half-time since Burnley were forced to do so in January 2015.
3 - Manchester United are the first team to make three substitutions in the first half of a Premier League game since Burnley in January 2015 vs Newcastle United. Ailing. #MUNLIV pic.twitter.com/tjWhNuxLMy— OptaJoe (@OptaJoe) February 24, 2019
The Red Devils had been hampered by injury before the game, too, with Nemanja Matic ruled out for up to a month, forcing Solskjaer to call on Scott McTominay to start in midfield.
With the battle for fourth place in the Premier League heating up and the second leg of his side's Champions League last-16 clash against Paris Saint-Germain coming up on March 6, Solskjaer will be sweating over the fitness of some of his key players.
Herrera had been used intermittently earlier this season under previous coach Jose Mourinho but has made himself a first-team regular under the Norwegian, while Mata has been in and out of the team in recent weeks.
Opponents Liverpool did not get through the first 45 minutes injury free, though. Jurgen Klopp's team were dealt a blow before the break when Roberto Firmino had to go off, with Daniel Sturridge coming on in his place.