Humphreys thrilled with defence
Gloucester's Director of Rugby, David Humphreys, praised his side's defence after they held off a strong second performance from Connacht to qualify for the semi-finals.
Two pieces of enterprise from James Hook created Gloucester's tries scored by Charlie Sharples and Bill Meakes with Greig Laidlaw adding two conversions.
Connacht's points came from a penalty try award converted by Jack Carty.
Humphreys said: "Ultimately our defence won us the game. After a five day turnaround, we were very good in the first half but we tightened up in the second half and made a few errors.
"It was very nervy at the end and it was a massive relief to win but that's what knock out rugby is all about. It's a reward for the amount of hard work we've put in this season."
Humphreys singled out Hook and Matt Kvesic for their outstanding efforts on the night.
"When James plays well, we play well. We see them every week and both are quality international players and therefore we'd love to see them represent their country again."
Despite the defeat, Connacht's head coach, Pat Lam, was delighted with his team's performance.
"I'm proud of the guys as they are a very young group who are very resilient and keep coming back," he said.
"Gloucester is always a tough place to come and they've got a lot of big game players. We didn't exit well and gave away soft tries in the first half but at half-time the boys were determined to get back into it so we were much more ruthless after the restart."
Gloucester now face Exeter or Newcastle in the semi-final at Kingsholm in a fortnight with Humphreys looking forward to the challenge.
"We are delighted to get another big game for Kingsholm. We are moving in the right direction and our results at Kingsholm have been improving since the New Year. We don't mind who we play as we should always be concerned about our own game."