"We got ahead 20 minutes into the second half, scored a good couple of tries and upped the pace a bit," said New Zealander Marsh, who is leaving Clermont at the end of the season after nine years in French rugby.
"But then the crowd got behind them and in the last five or ten minutes it was a struggle and we had to dig deep to get there in the end.
"Our coach Vern Cotter has brought in a lot of discipline. We have shown on several occasions this year that we have kept calm and stuck to our game plan. We had our moments when we struggled, but we dug deep."
ASM Clermont Auvergne are now automatically in next season's Heineken Cup and Marsh believes they will challenge hard in the latter stages of European rugby's premier club event.
Marsh himself is just a few weeks away from finishing a distinguished rugby career in France and he is hoping to claim some more silverware before he leaves.
"My European career is not finished because we still have a couple of weeks left," he said.
"The big goal for us is the French Championship which we have never won. We will celebrate this but then start looking forward to our next championship game before our semi-final in a couple of weeks.
"I have been here nine years now and France has given me a lot. I have grown on the rugby field and as a person so I certainly owe a lot to France and my club ASM."