Van Graan said he was “incredibly proud” to coach his team, who dominated their hosts for long periods, and their bonus-point victory booked their place in the tournament’s quarter-finals.
Joey Carbery led the way with a 26-point haul and Munster outscored the Cherry and Whites by five tries to two.
After the match, Van Graan couldn’t hide his delight and sang his charges praises.
“I’m incredibly proud to be the coach of a team who can put in an away performance like that,” he told RTE.
“I thought they were clinical, yes there were small things to work on but to get away first with a win here and that a bonus-point was pretty important, I’m really happy about that.”
Van Graan believes there were two moments in the match which proved decisive in the end.
The first one came on the stroke of half time when Rory Scannell scored a converted try – after patient build-up play – which gave the Irish province a 20-3 lead at the interval.
The second moment was early in the second half when Munster’s defensive line were forced onto the back foot as Gloucester took the ball through 35 phases before Ollie Thorley crossed for a try after gathering a well-timed pass from Danny Cipriani.
“I think there was two big moments in this game for me,” added Van Graan.
“Firstly that try just before half-time, we worked so hard on our patience over the last three weeks and it really paid off. That was a crucial try in the complexity of the game.
“And then even though we conceded a try off defending for 35 phases, I thought we got stronger after that and that gave us a lot of belief.
“I think Joey and Conor (Murray) managed the game pretty well and every time they scored, we responded with a score ourselves and I’m very happy with the win.
“There’s a certain window in a game of rugby that you’ve got to attack and I thought we attacked it quite well today.
“We were under tremendous pressure from the start of the game, they went to the corner straight away and we kept them out, that was a big turning point.
“The works not done, we’ll take the win and enjoy it tonight, you’ve got to enjoy every single game in rugby and it’s only Friday night now so the weekend comes at a good time for us. We’ll travel back and start again on zero on Monday.
“We’ve got a massive game again next weekend against Exeter, a team I respect a lot, possibly with some of the best attacking in world rugby and it will be a massive challenge.”