Just two days after drawing at Manchester United, the Premier League leaders were made to work hard for victory before prevailing 2-1 at Greenhous Meadow on Tuesday to reach the quarter-finals.
Andy Mangan levelled for the brave League Two hosts after Didier Drogba had opened the scoring, but a Jermaine Grandison own goal eventually settled the fourth-round tie.
"The four players who played on Sunday gave an unbelievable example for the others - Didier Drogba, Filipe Luis, Gary Cahill and Oscar were brilliant," Mourinho told Sky Sports.
"You have people like them, plus Petr Cech and [John Obi] Mikel, who have not been playing regularly but gave a great example of professionalism.
"That gives the kids like Andreas Christensen and Nathan Ake a perfect example, so I'm really happy as I was expecting a difficult match."
Mourinho revealed he hopes to have Diego Costa and Ramires back to face QPR at the weekend, but Drogba again did his bit up front against Shrewsbury, having also netted at Old Trafford.
The Ivory Coast forward commented: "It was a difficult pitch, difficult weather and fantastic opponents who gave everything - they created a difficult game for us.
"It was difficult for the players who have not played a lot this season and for those who were playing on Sunday, but with our experience we finally won the game."