Wrexham co-owner Rob McElhenney revealed he was left in the dark over their FA Cup shock after television coverage failed in the United States.
Meanwhile Ryan Reynolds said he was "totally speechless" at the 4-3 win.
Wrexham's reward is a home tie in the fourth round against another Championship side, Sheffield United.
National League Wrexham knocked Championship side Coventry out of the FA Cup in a seven-goal thriller.
Sam Dalby and Elliot Lee got Wrexham off to a dream start. Thomas O'Connor grabbed a third before Paul Mullin's penalty looked to have sealed the win at 4-1 with Coventry's Jonathan Panzo sent off for handball.
But they had to survive a nail-biting finish, after Coventry hit back twice, to reach the FA Cup fourth round for the first time since 2000.
Owner McElhenney revealed on social media he missed the final agonising moments only to be told by jubilant Dragons fans that they had held on for a remarkable win.
Fellow owner Reynolds had no such problems watching the game but did struggle to sum up his emotions.
He tweetedexternal-link: "I'm completely and totally speechless. What a club. What a town. What a win. @Wrexham_AFC forever."
Manager Phil Parkinson previously took League One Bradford City to the FA Cup quarter-finals but said this win was "up with the best" moments since arriving at Wrexham 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."
He added: "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."
The fourth-round home draw against Sheffield United, to be played on the final weekend of January, was not the tie that match-winner Mullin had been hoping for.
The striker, a boyhood Liverpool fan, was desperate for a trip to Anfield after maintaining his record of scoring in every round of the cup this season.
He said after beating Coventry: "It's a great feeling to be in the fourth round. I've come to love this club and days like this are amazing.
"The fans deserve this after keeping the club going. There has been a lot of attention on the club recently and days like this are the reason why."