Nemanja Matic's injury-time winner completed a 3-2 comeback for the Red Devils, who moved back into second place in the Premier League as a result, and Mourinho said some harsh words were shared at the interval, per Sami Mokbel of the Daily Mail:
"I cannot tell you half of the things I told my team at half-time because there would be lots of bleeping on television.
"There were a few strong words at half-time relating to their attitude and the intensity of the game.
"To come back from 2-0 down away from home against a team that is desperate for points, it gives us a great feeling."
Andros Townsend's deflected strike in the 11th minute set United back, and their initial reaction after half-time was far from ideal as Patrick van Aanholt snuck down the left to beat David De Gea and double Palace's lead.
Chris Smalling's header and a patiently taken Romelu Lukaku strike levelled the contest before Matic's looping half-volley settled the result, marking a career first for Mourinho in the process, per OptaJoe:
United's lack of intensity was apparent in Van Aanholt's goal soon after half-time, when Jeffrey Schlupp showed initiative to take a quick free-kick and free his Dutch team-mate inside the visitors' half.
The concession of that near-post strike indicated the attitude and intensity was still lacking for United after Mourinho's team talk, and Rob Dawson of the Manchester Evening News said substitutions played a key role:
United welcomed pressure close to their own box for Palace's first, and Schlupp spotted Antonio Valencia pushed up before timing his quick free-kick to perfection as Van Aanholt sprinted through onside for the hosts' second.
Mourinho was particularly critical of his side's lack of defensive awareness after Van Aanholt beat De Gea at this near post, telling Sky Sports (h/t Tom Doyle of the Evening Standard): "That disgraceful, childish second goal changed everything. But the players kept an amazing attitude."
The introduction of Juan Mata for Ashley Young after 67 minutes in particular looked to provide the guests with a calming presence moving forward with the ball.
Alexis Sanchez had an off night by and large and was dispossessed eight times, per WhoScored.com—at least four times more than any other player on the night.
Mourinho's frustrations were evident when he kicked a water bottle in the away dugout before immediately apologising to officials in an apparent attempt to escape any potential punishment, via Sky Sports MNF:
Sky Sports MNF @SkySportsMNF
WATCH: It was an eventful night for Jose Mourinho at Selhurst Park! 😂 He kicked an empty water bottle into the crowd and later fell over in the dugout as his side were chasing a winner! 💦 Watch it and find out what he had to say here: https://t.co/9T4632c6r4 https://t.co/gc3RJYsXap
The United boss went on to acknowledge his players "accepted the risk" in the second half, best summarised in Matic's game-winning strike, his first goal for the club.
Monday's victory at Selhurst Park was akin to the comebacks that became almost commonplace under the reign of former United manager Sir Alex Ferguson, putting them in good spirits for the visit of archrivals Liverpool on Saturday.