The Belgian's mishap condemned Mourinho's side to their ninth defeat in all competitions this season and saw the holders exit the tournament in the fourth round.
Defending his team's performance, Mourinho said: "What the players did tonight is face some people that write and speak, and said: 'You are stupid'.
"What some people write and say is really bad for the players. Maybe they think my players are like them when they were players. My players don't do that. They tried everything."
His comments come hot on the heels of a 2-1 defeat at West Ham United where he faces a Football Association misconduct charge after being sent to the stands, and ramped up the pressure on the Portuguese ahead of Saturday's Premier League home game with Liverpool.
With Chelsea currently 15th in the league table and third in their Champions League group, British newspapers have speculated that Mourinho could be sacked if their fortunes do not improve quickly.
At Hillsborough, Arsene Wenger's Arsenal were well beaten by Championship side Wednesday.
Ross Wallace put Wednesday ahead after 27 minutes and then teed up Lucas Joao for the hosts' second goal shortly before half-time, with Sam Hutchinson completing victory early in the second period.
Asked how his young fringe players had handled the occasion, Wenger delivered a scathing assessment, telling Sky Sports: "It was too high for them. They are not ready to play at this level, none of them."
On the injuries his team suffered, he added: "We are short now because we lose Chamberlain today, we lose Walcott and we have already a few injuries.
"It is a big blow for us, of course to lose the game, but even more for the other competitions, which are very important for us, to lose two players of that stature."
It was Wednesday's second Premier League scalp in this season's competition, following their third-round win at Newcastle United, and brought Arsenal's run of four successive victories to an end.
Wenger made eight changes to the team that beat Everton 2-1 on Saturday for the trip to Hillsborough, which was a repeat of the 1993 final.
Oxlade-Chamberlain was one of only three players who kept their places, along with Petr Cech and Olivier Giroud, but he went off in the fifth minute after pulling up while running along the touchline.
Walcott replaced his England team-mate, but he in turn was forced off 13 minutes later with an apparent calf injury.
