Johann van Graan was delighted that Bath were "enjoying the journey together" after they completed the second leg of a possible trophy treble.
Bath's 37-12 victory over Lyon saw them lift the EPCR Challenge Cup in Cardiff to clinch their first major silverware since winning the same competition in 2008.
They add the Challenge Cup to Premiership Cup success earlier this season and the ex-Munster head coach is two victories away from leading the side to league title glory for the first time since 1996.
"This is a moment in time," Bath head of rugby Van Graan said. "We will enjoy what this trophy represents.
"We are enjoying our journey together and it is huge for the whole group. We all fight for each other.
"We have taken it step by step by step from the start and it is a group that wants to achieve together.
"Everyone has pulled together, every day on the training pitch and I give credit to the leadership group and all the players."
Van Graan’s team overcame first-half yellow cards for Sam Underhill and Will Muir at the Principality Stadium – they had 13 players for four minutes – to subdue dogged opponents and post the tournament’s biggest winning margin in a final since 1998.
Tries from hooker Tom Dunn, centre Max Ojomoh, prop Beno Obano and captain Ben Spencer saw Bath home, while Spencer’s half-back partner Finn Russell kicked four conversions and three penalties.
Spencer told Premier Sports: "I thought we showed a different level of intensity tonight that we’ve not seen this season.
"I am just so proud to be able to give the fans what they deserve after so many years of hurt.
"We speak a lot about working hard for each other and the yellow card period is something we pride ourselves on.
"When we go down to 14 it’s not an ideal situation, but to not concede in that yellow card period I thought was outstanding.
"The togetherness in this group is absolutely unbelievable. It’s something we spoke about before the game in just being the best version of ourselves tonight and not playing the occasion, just playing the game."
Lyon led through wing Ethan Dumortier’s early score, with number eight Arno Botha also touching down – as fly-half Leo Berdeu added one conversion – but Bath were comfortable winners.
And they appear to be on an unstoppable roll ahead of a Premiership play-off in two weeks’ time, when their opponents could be west country rivals Bristol.
Lyon coach Karim Ghezal said: "We didn’t score when they were down to 13. They had two yellow cards.
"One of them was rather dodgy. I will never complain about refereeing.
"It is always hard losing a final. A lot of energy went into this tournament and we came here to win the cup. Bath are a very strong team, but we lacked efficiency."
