Harlequins staged a dramatic late comeback against Northampton to reach the first Premiership final in their history on Saturday, with Marler's converted try four minutes from time sealing a 25-23 victory.
Last year, Harlequins snatched a similar last-gasp victory over Stade Francais in the Amlin Challenge Cup final and they have beaten both Munster and Toulouse away.
Marler believes Harlequins drew from those experiences after finding themselves eight points down to Northampton with 14 minutes remaining.
And the England prospect believes those experiences mean Quins are ready to tackle the Tigers, who beat defending champions Saracens to reach an eighth consecutive Premiership final.
"I am just buzzing for Twickenham now. The final will be massive," Marler said.
"We have had great games against Leicester. We will front up.
"This pack started against Munster away, it started in the Amlin final. We have played in big games. We have started to mature now.
"Unfortunately it took Northampton's try for us to turn around and say: 'We need to pull our fingers out here'.
"We didn't panic, based on those results we had before, and we went out and did it."
It was heartbreaking for Northampton, who should have closed the game out after Lee Dickson had finished a 50-metre attack to put them 23-15 ahead but slipped to a third Premiership semi-final defeat.
But, over the course of the season, Harlequins deserved a place in the Premiership final having been top of the table since mid-September.
They only lost four league matches all season but, crucially perhaps, two of them were to their final opponents Leicester.
Despite dominating impressively up front, Harlequins were far from their best against Northampton in a game which failed to live up to expectations for the first 70 minutes.
But with the win on the board, the quality of performance did not concern O'Shea in the slightest.
"My Dad won a lot of All-Ireland finals with Kerry and he always said that great semi-finalists never make good finalists," O'Shea said.
"We have a performance left in us."
Northampton left the door ajar for Harlequins when Ryan Lamb, who had kicked everything else all day, missed the conversion to Dickson's try.
Harlequins' comeback began with Nick Evans slotting his sixth penalty and was completed by a remarkable lineout drive which saw virtually every player in the maul.
Not only were Northampton driven backwards but they were driven towards the posts, making the winning conversion a formality for Evans.
"I saw Nick Evans on my left and Karl Dickson on my right," Marler said.
"I thought: 'This is it lads, sod throwing the ball about, we are just going to maul'! It was a great team effort.
"People expect us to the throw the ball about, it is what Harlequins have been known for over the years.
"We like to think we can still do that but we want an all-round game. The scrum is a big area we have worked on this year and so is the maul. That showed out there."
Northampton fell short again with the manner of the defeat in a third consecutive Premiership semi-final particularly agonising.
They were missing five England players through injury, including Chris Ashton who has now played his final game for the club. Roger Wilson, Andy Long and James Downey are also leaving this summer.
Northampton director of rugby Jim Mallinder was anxious to put the Saints' achievements of recents into perspective and he is optimistic about the future.
"I would be really disappointed if we were finishing eighth or ninth in the league every year. We are not. We are in Europe every year, we are in semi-finals and we are giving ourselves the chance," Mallinder said.
"We made the Heineken Cup final last season which was a tremendous effort for us. We are in a decent position. We are not making that many changes in the summer and we have a few good players coming in.
"That will stand us in good stead for next year."
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