Rovers have accounted for many a Premiership big shot in recent seasons and the boss could not hide his delight that he can now prepare for Cardiff safe in the knowledge that a place in the last eight is booked.
"I am delighted with the performance and the result obviously," said Glenn. "What was a potential banana skin ended up with us seeing them off with relative ease.
"That's not to say it was easy. Credit to Dave's team, at 4-0 down in the last minute they were still giving it exactly what they were giving it in the first minute - and that's a credit to them.
"That's probably why they've had so many cup scalps over the past few seasons. But today the difference in the divisions showed and we were delighted with the performance. We are now in the last eight and that's what it was all about - getting through into that hat."
Glenn brushed aside the suggestion that the result had buried the ghost of Tranmere winning 4-3 against Southampton while he was in charge of the south coast outfit - pointing out that this was the second time the Birkenhead side had been overcome this season.
"To be fair that is the double we've done over Tranmere in the cups. I think the first one was more putting it to rest, being on the same ground. Two 4-0 wins though, you can't ask for more than that and two clean sheets.
"This wasn't about me, this was about us as a club getting through to the last eight and we've done it with a touch of class."
Gus Poyet fulfilled Glenn's wish of sending the fans home happy with his goal nearly right on time.
"It's buoyant here at the moment. We were 3-0 up and won the game and I said to John wouldn't be nice to get another one right late so it gives the crowd a lift to go home and, bang, Gus was right on cue.
"So they've gone home with a lot of belief and looking forward to the final - and so is the team."
Glenn added that Sergei Rebrov was missing from the squad due to a small Achilles strain.
Glenn was a happy man that the boys stylishly avoided slipping on a potential FA Cup banana skin against Tranmere on Sunday.