This was the club's first European outing in a decade, yet many fans left the ground once their side went six goals behind in the first minute of the second half.
United were defending a 1-0 lead from the first leg, but ended up on the end of Scottish football's joint-worse defeat in continental football.
"For every plaudit and praise we received in the aftermath of last Thursday, we will deserve every bit of criticism we get on the back of that," Ross told BBC Radio Scotland.
"We played against a good team in a tough venue but we conceded six goals in 26 minutes. That's not good, irrespective of the opponent.
"I would like to apologise to the travelling fans because we should be better than that."
United looked composed in the opening stages of the match, before collapsing at the back and conceding six goals in a space of 25 minutes.
"All the discipline we showed in our play without the ball last week, we didn't do as well, and we didn't deal with the period of adversity well in the first half," Ross added.
"Heads become foggy, because they are a good team, and when their tails are up it becomes easier for them.
"But we needed to be tougher in that period and almost look at it like five-minute blocks to get us through.
"But we became ragged and loose, out of possession, never mind in possession. When you do that, you will get picked off against good sides.
"The goals were poor in terms of some of the decision-making. It's a sore, sore night for us. Pride is damaged by that."