Christian Doidge scored Hibs’ second to seal a place in the May 22 final – but replays showed the flag should have been raised for offside and referee Bobby Madden should have chalked the goal off.
It wasn’t the only frustration of the performance for Mellon who also didn’t think his side “showed enough personality” to defeat Jack Ross' team. The Hibs boss will return to the National Stadium to face either his former club St Mirren, or Betfred Cup winners St Johnstone, in the final.
But ruing the offside decision, Mellon said: “You've got to get them right. They strut about all afternoon, don't take control of the time-wasting or the gamesmanship. You expect that to be dealt with by the ref.
"He never did that all day but you've got to be careful what you say because you get yourself into trouble and I'm not prepared to do that.
“But at 1-0 you're still very much in the game, you know you're going to get to a time when it becomes tense and if you can take the game into that place you'll get an opportunity to maybe get that equaliser that takes the game into a different stage.
“Listen, I have to be honest and say Hibs were worthy of going to the final but those wee moments have to go your way and you expect them to get dealt with better.”
Mellon's ninth-placed side now have the opportunity to finish seventh in the Premiership a year after promotion with two games left in the league campaign.
He added: “We'll learn from the experience but we need to show better qualities, not just with the ball but without it, better mentality, so that when we get the opportunity to come here again we're better.
“Games like Saturday’s can only help us in moving the club forward. That’s what we’ll try to do.
“These boys have played a lot of Championship football and to come in and get to a major semi-final and stay up so comfortably is a massive step forward for us.”