The Red Dragons played for nearly 80 minutes with ten after Sam Wedgbury was red carded in the early stages of the derby match.
Rovers couldn't capitalise on their 13th minute numerical advantage and even slumped to defeat when Chris Holroyd struck near the hour mark.
Tranmere's terrible start to the season sees them lagging behind, sitting just two points outside the relegation zone and the manager gave an honest reflection after.
"It's a sore one for us, we know how much this game means," said Mellon, who took the club to the Vanarama National League promotion final last season.
"To play against ten minute for so long and not be able to overcome it is very disappointing.
"I think with the way we are at the moment, Wrexham going down to ten men was maybe something that we didn't want to happen. We couldn't get in a position to capitalise on that.
"We look low on confidence. I think we have to be fair and say that. But it's my job to fix this.
"To not score in so many games now I think tells a lot of the story and it's a big frustration for us all.
"We miss that little bit of quality or that little bit of guide to find ourselves a goal. We just didn't have it and when we switched off from a corner we were punished."
Mellon knows it is now time to stand up and be counted - and says his squad is good enough to still challenge.
"We now have to fight, show character and work hard to try and address this," the Prenton Park boss said.
"I still believe in the squad. There hasn't been many chances from the side who were so rampant last season. Things at the moment are just not going our way."