Shaw set up goals for Aaron Wan-Bissaka and Edinson Cavani before being hauled off for a well-deserved rest at half-time, and will likely be back in the team when the Red Devils play host to Everton this weekend.
Alex Telles moved to Manchester from Porto in the summer transfer window to provide Solskjaer with another option of the right of the defence, but he hasn't had much of a look in due to Shaw's impressive recent form.
Irwin claims the Brazilian's arrival forced the 25-year-old to raise his game, and he doesn't feel there is anyone else in the top-flight matching his level of performances right now.