The Easter Road side will meet Steven Gerrard's team in November after progressing to the last four of a domestic tournament for the fifth consecutive time.
The upcoming semi-final represents the first Hampden showdown between the teams since the dramatic 2016 Scottish Cup final, which Hibs won 3-2.
Ross said: "Whoever we got, it was going to be a tough game. I'm excited by it.
"The big difference from the previous semi-finals is the size of the crowd that will be there and a good atmosphere will be generated.
"It's a brilliant tie. Rangers won three of the games last season but I thought we were highly competitive. It's about taking that next step.
"We play Rangers in the league before the semi-final as well which will be a good barometer to see where we're at as well. It will give us some indication of how we plan for that game.
"There's a lot of football still to be played before that time. It's just brilliant for the players to be in another semi-final."
Ross was thrilled with his team's performance as first-half goals from Joe Newell, Scott Allan and Martin Boyle put the tie beyond United.
He said: "I was really pleased with a really strong performance. We were ruthless in the first half when the game was open. They gave up a couple of opportunities but we carried that attacking threat that we have. We have scored a lot of goals this season and we have pace and creativity in the final third."
United manager Tam Courts felt the officials were wrong to award Hibs the penalty from which Boyle scored Hibs' third, while home goalscorer Peter Pawlett also had a goal dubiously ruled out at 3-1.
He said: "I'm really disappointed by that, really disappointed for the players. Mark Reynolds has had to spend some time on the bench, comes on and performs so admirably well, and then has to deal with an unjust penalty decision. I'm really disappointed for him.
"Then Peter Pawlett, who I think is in the form of his life and is a real joy to watch, it would have been a cracking finale if we had been awarded that legitimate goal and took it down the home stretch. Unfortunately we never got that opportunity."