Shaw has had a mixed start to the campaign and lost his place in the starting line-up after Mourinho publicly criticised the 21-year-old following United's loss at Watford last month.
"It's normal you're frustrated on Sunday because I would have loved to play in that game (against Chelsea)," Shaw told British media. "But it obviously wasn't meant to be and at the end of the day it is the manager's decision.
"Obviously with the injury with Eric now it might be my time to step up and show the manager what I can do and that he can trust me."
Shaw started at left back on Wednesday in United's 1-0 win over City in the League Cup.
United, who are seventh in the table, host 14th-placed Burnley in the Premier League at Old Trafford on Saturday.
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by Peter Rutherford)
