Last season the 1999 champions won all four of their Pool games and the first leg of their Round of 16 tie with Stade Toulousain, but agonisingly missed out on a place in the quarter-finals by a single point when the French side triumphed 50-49 on aggregate.

However, Madigan, who can play at fly-half, centre or full-back, pointed out that their narrow failure only made Ulster realise that they’re getting better.

“We were within a point or two points of qualifying for the quarter-finals,” said the 33-year-old. “We won five out of our six games.

“In the previous format, winning five out of your six games would’ve got you a home quarter-final against one of the weaker teams. Five out of six last season left us out of the competition.

“Sometimes in sport you’ve got to get close to winning one to realise that you’re good enough to win one.

“I think that’s where Ulster are now. We’ve got close, we’ve lost finals, we’ve been close in knockouts. We feel we’re ready this year to step up and go one step further.”

Madigan, a 30-time Irish international, underlined that he and the rest of the Ulster squad cannot wait to play in the Heineken Champions Cup again.

“You arrive in on the Monday of a Heineken Champions Cup week and there’s a different smell about the place,” he revealed. “You walk out onto the training pitch, you see the European balls, you’re in different kit.

“The attention to detail goes up, your recovery improves. It’s just a different energy.”

The United Rugby Championship side visit Gallagher Premiership club Sale Sharks in their opening Pool B fixture on Sunday and Madigan is sure it will be a tight clash between two solid teams.

“Obviously, from playing in the Premiership, I keep a very close eye on it and I’ve been impressed with them this year,” the former Bristol Bear said of Sale. “They have a really strong pack, so for us, it’s going to be about getting parity.

“If we don’t get that, we’re going to struggle, because our super strength is without doubt in our backs. If we can get good quality balls to the likes of James Hume, Rob Baloucoune, Mike Lowry and Jacob Stockdale, we know we can compete with the very best.

“It starts up front, from [the front] five, and Sale, I think, are one of the best sides in the Premiership in that facet of the game.

“It’s going to be a real challenge for us and it’s difficult starting away from home. It’s a competition you need to build momentum in and if you lose that first game, you can find yourself under big pressure very quickly.”

Ulster Rugby back Ian Madigan believes the Irish province can “compete with the very best” in the Heineken Champions Cup as they try to end their long wait for an EPCR title.