Reynolds and Mac celebrated five years in charge of Wrexham last month.
During their spell as owners, the Red Dragons have risen from the National League to Championship play-off contention thanks to three successive promotions.
American actor Mac, 48, described commentating on Wrexham’s game against Swansea as the “most rewarding professional experience of my entire life”.
Wrexham won the game 2-0 to boost their hopes of reaching the Championship play-offs while dealing a blow to Swansea’s slim top-six chances.
“With the production being done by Rob and Ryan’s own production company, all of the guests and focus was on their team, there were celebrations with David Prutton – the face of Sky’s EFL coverage – and the advert for the commentary of the game failed to mention that we were playing at all,” added Gorringe, who was named Swansea chief executive just over a year ago.
“It felt to myself and a number of members of our staff that we were very much an afterthought and that our hosts were given priority at every opportunity, and as a club we would strongly suggest that greater critical thought is given to how these situations are handled moving forward.
“This is a position that I will discuss with the EFL next week.”
Sky Sports insisted that contrary to Gorringe’s statement, it was responsible for the production of the Wrexham-Swansea coverage.
Sky Sports also revealed 40% of the in-home viewers of the game opted to watch the alternative stream featuring Reynolds and Mac.