The Republic of Ireland defender was sent off for deliberate handball as he punched away substitute Tom Elliott’s goalbound header with five minutes of Saturday’s game remaining.
Although Egan’s decision looked to have been vindicated when Ben Marshall missed the resulting penalty, Jake Cooper scored a last-gasp equaliser for Millwall as the Blades lost further ground on Leeds United in the race for second place.
Egan will subsequently miss Friday’s clash with Nottingham Forest at Bramall Lane – at the time of writing, the FA had not yet confirmed the exact length of his suspension – but Wilder insisted he had ‘no problems’ with the decision, adding: “It’s an instinctive situation where John deals with it, and we have got to get on with it.
“We've lost players before; we missed Jack O’Connell for a few games and Chris Basham for a few games recently and we have got to deal with it.
“It’s an opportunity for someone to step in and we’ll deal with it. John has been excellent, losing Bash wasn’t great and then the skipper, too.
“We’ll assess those but in terms of injuries and suspensions, it’s a real disappointment. And the fact we didn’t get a big three points was, too.”
United’s misery was compounded on Saturday by the departure of Basham and skipper Billy Sharp with hamstring injuries, with Wilder and his coaching staff facing an anxious wait to discover if the pair will be available for the Championship run-in.
After Leeds extended their lead over third-placed United to three points by beating Sheffield Wednesday on Saturday evening, Wilder will be aware that any more slip-ups in the four remaining games could condemn his side to the play-offs as they chase the Premier League dream.
"When Millwall went a goal down they had to show more ambition, but we just went backwards instead of trusting the shape. We went backwards in thought and in play and paid the price,” Wilder added.
"After the goal they deserved a point, but we never showed enough ambition to go on and score the second, which is uncharacteristic from our team.
"We played safe and didn't go for the jugular. We played backwards and square and sat in, so I'm not surprised they got back into the game and deservedly so.
"It's stinging that we didn't get those extra two points."