The National League side were knocked out in the fourth round replay at Bramall Lane, with stoppage time goals from Billy Sharp and Sander Berge taking the hosts through.
Anel Ahmedhodzic had put Sheffield United ahead early in the second half before Paul Mullin equalised from the penalty spot.
But Mullin missed a second opportunity to convert from 12 yards with 20 minutes to go, allowing Sharp and Berge to take their side through to an encounter with Tottenham.
Reynolds, who co-owns the Welsh club with fellow actor Rob McElhenney, had been in attendance at the County Ground for the original tie as Wrexham were denied a fifth-round place by John Egan’s late equaliser.
The Hollywood star extended special thanks to a healthy travelling contingent of away fans who made the Tuesday night trip to Yorkshire.
“So proud of these boys,” Reynolds tweeted. “And the 4000 plus away supporters who gave it all.”
Wrexham are currently second in the National League, three points behind Notts County but with two games in hand on the league leaders.
McElhenney, co-creator and star of long-running sitcom “It’s Always Sunny in Philadelphia”, also hailed the efforts of Phil Parkinson’s side.
— Rob McElhenney (@RMcElhenney) February 7, 2023
“I could not be more proud of those men than I am right now. They gave it absolutely everything,” the actor tweeted, before adding in a subsequent tweet: “Now let’s go and win the f****** league.”
Wrexham next host Wealdstone on Saturday.