The Ospreys rightly received plenty of plaudits for the 17-12 win at the RDS but critics have often been quick to question the region following a number of heart-breaking European exits.
And director of coaching Johnson and head coach Holley hope the achievements of Ryan Jones and co will now be properly recognized.
"It's about time people gave them the credit they deserve," said Johnson, who joined the Ospreys last year.
"They've done unbelievably well since Biarritz. They've gelled together as a team and as a squad and probably showed what sort of people they are.
"It's nothing to do with me, it's got all to do with them and they've been fantastic."
The Ospreys are the first side in the history of Magners League rugby to win a hat-trick of Celtic crowns, with last weekend's success following similar triumphs in 2005 and 2007.
But despite also picking up the EDF Energy Cup in 2008, a great deal of focus has been on the manner in which the Ospreys have been knocked out of continental competition at the quarter-final stages in each of the last three years.
And although Holley admits that his side are desperate to lift the Heineken Cup, he believes critics should be patient and realize that Rome wasn't built in a day.
"Last year in particular, we went through some pretty difficult press conferences," said Holley.
"We do feel that we've got what we deserve this year. We've played some really good rugby, worked extremely hard as a group and Johnno's come in and really cemented that.
"That's four trophies in seven years - that's not a bad strike rate. You all know how long it's taken Munster and Leinster to consistently perform.
"For us, that's a good strike rate and we get very little credit for it back home. We're seen as something that we think we're not. We're not moaning about it - in adversity sometimes character comes out and that's what we've seen at the Ospreys this year.
"We're a great bunch, we worked hard and we're doing Wales proud."
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