Exeter Chiefs head coach Rob Baxter said it was a "privilege" to be part of a club that "never goes away" after his side won the Champions Cup.
Baxter, who played for Chiefs before taking over as head coach in 2009, said the club have always "stuck at it".
"We have always just ticked along," Baxter told BBC Radio 5 Live.
"It's not always been easy and there have been quite a few years in the Premiership where we have lost more games than we have won.
"Being part of a rugby club that decides to stick at it no matter what comes at you is a real privilege. I played in two and coached two [Championship] finals that we lost at Twickenham, but we never went away."
The game was played behind closed doors at Ashton Gate in Bristol and the 49-year-old Devonian said he became emotional while speaking to his wife on the phone after the full-time whistle.
"She was bawling," added Baxter.
"It's an amazing thing, she has watched me play in some pretty dire places compared to this.
"There were probably more tears for the lads today because people [friends and family] aren't here and they are removed from them."
The Chiefs opened up a healthy lead before Racing began to find their rhythm and eventually reduced the deficit to just one point with 10 minutes remaining.
Exeter lost replacement prop Tomas Francis to the sin bin for a deliberate knock-on in the 71st minute, but Joe Simmonds' penalty sealed victory with the last kick of the game.
"We took a lead and it felt relatively comfortable and I was thinking 'when are we going to start working?'," said Baxter.
"I was concerned with the way we defended and I thought we defended as poorly today as we have done for a long time.
"But finals are about winning and, by hook or by crook, you need to be in front when the scoreboard ticks over."
'This just doesn't happen to people like us'
Simmonds' older brother Sam, who has played for England and was named European Player of the Year after the game, said the victory was the greatest moment in his career.
"Playing for England is huge and I'm very proud of my achievements, but to be able to play in the top tier European final with my brother, and with him getting man-of-the-match, is unbelievable," said the number eight.
"This just doesn't happen to people like us.
"It's an unbelievable effort by the 50-man squad. It's a journey the club has been on for over 10 years and we have achieved the goal."
Exeter face Wasps in the Premiership final next weekend (24 October) and Sam Simmonds says the players are "looking forward to potentially winning the double".
Those comments were echoed by full-back Stuart Hogg, who said he joined the club from Glasgow Warriors in 2019 "to win trophies".
"Everything about the club excited me and I'm living the dream," said Scotland captain Hogg.
"We are fighting for that title next week and we have a lot to work on for the Wasps game, but we will enjoy this one now and worry about that on Monday."