Their hat-trick of Heineken Cup years comes on the back of 15 seasons of watching on with envy while the big guns battled it out away from Galway and Muldoon admits that the chance to test themselves against the very best will never grow old.
"It's very hard to be on the outside looking in. When you're on the inside and involved in it you see how special a competition the Heineken Cup really is. We certainly won't be taking it for granted," said Muldoon.
"Everyone - supporters, management and players - looks to see what weekends the Heineken Cup are on and that shows you the sense of excitement. The whole province will get behind us.
"Galway has really embraced it and Connacht as a whole has really embraced the Heineken Cup as well. Our fans want that and expect that now. Like the players, they've had a taste of the Heineken Cup and they don't want to go back to any other competition.
"It's the top tournament in Europe and one of the top competitions in the world. It's a great tournament to be in and we hope that we're in it for many years to come. We have to thank Leinster for that a lot over the last few years but we are improving and we feel that we do deserve to be in there."
Connacht beat then Amlin Challenge Cup holders Biarritz Olympique and Italian newcomers Zebre (twice) in last season's competition as they built on a fine win over soon-to-be English champions Harlequins in their opening campaign.
They ran Quins close again in Galway last season and twice came within a score of toppling Gloucester a year earlier to prove that they are more than comfortable at the top level.
So what next for Ireland international Muldoon and his troops? Can they push on and challenge for qualification for the knockout stages this time around? That certainly looks a tough ask given that they find themselves in the same pool as French giants Toulouse and former Aviva Premiership kings Saracens, but with a new director of rugby in Samoan great Pat Lam and with a greater strength in depth in their squad after the return of Fionn Carr and the arrival of the likes of Exeter lock Aly Muldowney and the Chiefs' Super XV winning captain Craig Clarke, anything is possible.
"We've really come on in the last two or three years. Our squad has become massively competitive," added Muldoon, who is keen to see even more improvement in Europe this term.
"We're quietly confident that we can improve on last year. The teams we're drawn against are really good but we're confident that we can progress as a side and get better this year.
"We've lots of options in every position now and that's something we probably haven't had in the past. If one of our key personnel had got injured a few years ago it would have very bad for us, but we've got lots of options now.
"It's a massive challenge…but it's exciting. We're in band three for the seedings so you look at grade one and two and you realise that the quality of the teams that are in there is huge.
"Sarries have been trying to get up there and have certainly become one of the top European clubs. They've showed that they can play two completely different styles of rugby. It's something our fans will look forward to as well, as we haven't played them competitively in a long time.
"Saracens and Toulouse are the type of teams you want to be playing against. There's so much quality in this competition and that's what brings out the best in players. They're the standout fixtures and they're definitely ones you want to be involved in."