"The crowd was unbelievable," said Cheika, after the Leinster supporters made themselves known within a crowd of more than 66,000 at Murrayfield.
"I was quite shocked to be honest to see the amount of blue that was there on the way into the ground and in the ground itself.
"When games are tight, like we saw at Harlequins, at Croke Park (against Munster) and again here, the crowd are a factor. They were just unbelievable for us."
Cheika's side ran out 19-16 winners in the Scottish capital as they fulfilled a long term ambition of lifting the continent's most-treasured prize.
Leinster had often dreamed of Heineken Cup glory but, despite moments of brilliance including a stunning away victory over Toulouse in the 2006 quarter-finals, had never performed consistently enough to lift the coveted trophy.
A semi-final defeat to perennial rivals Munster in Cheika's first season was the closest Leinster had come to becoming Europe's top team before the class of 2009 finally got rid of their under achievers' tag.
The fact that they did so by beating high-flying Harlequins in the quarter-finals, crushing defending champions Munster in the last-four and by coming from behind to win Saturday's showpiece makes their success even sweeter according to Cheika.
"We've played the top two teams in England and the top team in the Magners League and we've been able to sneak a win in all of them.
"If you compile them all together, then it's been the best run we've had. In the context of where we've got to, they were a good few to put together because we've ended up in the final and we've gone on to win it.
"We've had a lot of great games though. Maybe some of them people wouldn't be covering. I remember when we had to defend our own line for 15 minutes against Connacht down at the Sportsground in an absolute hurricane.
"We've had a good run this year and we've been able to stay in big games. I just think we believed in ourselves to come back (against Leicester).
"We played quite well in the first part of the game. When we went behind, we started dropping off a few tackles in close.
"They started cranking up their machine, they started counter-rucking us and taking it hard at the line.
"They really started to try and dominate us but we were able to stay in there and come back."
Cheika joined Leinster almost four years ago to the day, and the Australian admits the province were taking a risk in appointing him to one of the most-sought after positions in Irish rugby.
His appointment may have been viewed with cynicism in some quarters but he believes his players have done him proud and have finally gained their reward for their continued hard work and dedication to the cause.
"They took a bit of a gamble on me because I didn't have a lot of experience so I just wanted to repay that faith by putting a bit of stability and structure in place. That's what I'm here to do," he said.
"The one thing I found was a group of players who were eager and hungry to be successful. They've gone about learning how to be that way and that's been a great rule so far."