The Red Dragons beat Coventry 4-3 to set up a fourth-round tie with Sheffield United.
But the actor was left in the dark during the final moments and took to social media to follow the closing stages of the match at the Coventry Building Society Arena.
Co-owner Ryan Reynolds was also shocked by the upset and said he was left “totally speechless” as Phil Parkinson’s side held on after the Sky Blues closed to within a goal after trailing 4-1.
And owner McElhenney said on social media: “The feed at ESPN+ went down!!! What’s happening????”
While Reynolds added: “I’m completely and totally speechless. What a club. What a town. What a win. Wrexham forever.”
McElhenney then took aim at Sheffield United, Wrexham’s fourth round opponents, labelling them “the enemy” in a tongue in cheek tweet.
He said: “I visited Sheffield last summer! The town was beautiful and the people couldn’t be more welcoming. They of course are the enemy now and their tyrannical reign through the Championship must be stopped a la Goliath. But lovely people.”
Parkinson, who can count an FA Cup run to the quarter-finals while in charge of Bradford City, said the win was “up with the best” moments since joining the club in July 2021.
“You have to savour these days,” he said, “It was a great occasion from the moment the coach arrived at the ground and the players saw all those 4,500 fans.
“Honestly, everyone felt 10 feet tall when they walked into the dressing room. The adrenaline that was pumping through the players’ bodies was a by-product of that great support.
“The league is most important but we’ve got a great history in the FA Cup and we wanted to respect that.
“It was an excellent performance and the players had to show different qualities over the 90 minutes.
“We played some fantastic football against a really strong Championship team to go 4-1 up. Dolby’s goal was a great move.
“But the referee made some strange decisions so it ended up being a lot tighter than it should have been.
“We had to dig deep in adversity to make sure those decisions didn’t spoil a great day for the club.”