United, who also lost centre back Eric Bailly to injury during the match, have a lengthy casualty list, with defenders Phil Jones, Chris Smalling and Marcos Rojo all sidelined along with top scorer Zlatan Ibrahimovic.
Shaw has endured a difficult time since returning from a double leg break that kept him out for nearly a year, with Mourinho publicly questioning his commitment and ambition earlier in the season.
United, who are fifth in the Premier League table, a point and a place behind Manchester City with four games to play, take on Celta Vigo in the first leg of their Europa League semi-final in Spain on Thursday.
(Reporting by Simon Jennings in Bengaluru, editing by Ed Osmond)
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