Graeme McDowell tees off on the 18th in the final round. Photo Eoin Clarke/www.golffile.ieGraeme McDowell can’t wait for another thrilling major championship roller-coaster ride and he’s already setting his sights on the Claret Jug following his gutsy runner-up finish in the US Open at The Olympic Club.

The 2010 champion battled back bravely from a nightmare start and gave himself a chance to force a Monday play-off with shock winner Webb Simpson only to see his 24-foot birdie putt at the last slip by the hole.

But after finishing tied for second with Michael Thompson, just a shot behind the winner, he’s all but sealed his third Ryder Cup appearance in Chicago in September and now knows he has the game to win more Majors.

Setting his sights on next month’s Open Championship at Royal Lytham and St Annes, McDowell said: “I have a couple of ‘Majors’ coming up in the next few weeks. I’m excited about the Irish Open at Royal Portrush next week and I am sure they will be expecting plenty from me now.

“After that I will probably take the week of the Scottish Open off and go to Lytham and prepare. I fancy a run at that Claret Jug, I do.”

Up 10 places in the latest world rankings to 11th, McDowell pocketed a cheque for €559,687 to climbed to fourth in the European Ryder Cup Points list.

But he also left San Francisco with something a lot more precious than money — renewed belief in his ability to compete for golf’s most coveted titles.

Asked what he would take from the US Open, he beamed: “I will take away a large cheque and I’m probably very close to locking my Ryder Cup place, which is more important to me. I will take a huge amount of belief in myself that I can compete on the biggest stage and win.

“To have the chance to win and come up one short, hitting it the way I was hitting it today - I wasn’t on top of my game in any shape or form - I believe I can win more Major Championships.

“I will take a huge amount of positives away from this week. I am disappointed, yes, but part of me is also very proud I battled back from a disappointing start.”

Tied for the lead with Jim Furyk starting the day, McDowell got off a poor start but fought back with a birdie at the 17th to setting up a chance to force a play-off.

It didn’t work out as he missed and shot a three over 73 to finish a shot behind the winner on two over.

Yet he headed for Portrush with his confidence on the rise after competing with what he described as he “B plus game.

While he admitted that nerves and the pressure of playing in the final group contributed to his poor start and conceded hat his bunker play is a weakness he must address, he can’t wait for another chance to test his mettle on the biggest stage in golf.

“My caddie made a great analogy about the US Open,” said McDowell, who loves the heat of battle. “It’s like a really fast, scary roller-coaster that you get on at the time and you’re not sure if you like it and it’s kind of scary.

“But once it’s done and you look back, you realise that you had a lot of fun and you would like to do it again, and that kind of sums up what it’s like to compete on the big stage at a Major Championship.”

Struggling off the tee on Sunday, McDowell was proud of the way he fought back not once but twice in the final round to go to the last with a chance.

Four behind at one stage, he got back to within a shot of the lead, dropped two more shots but then made a great birdie at the 17th to set up a hair-raising finish.

He said: “It was great to have an opportunity to compete and get in a playoff to win one of the greatest titles in the world having hit three fairways today. That’s just not good enough.

“But I hung in there and I will take a lot of pride from the way I stayed tough on that back nine

“There was never going to be any giving up. Two or three over was going to win this tournament at any stage. I was playing with the leader most of the day.

“Even despite my bad start I was never really that far away. I was just proud of myself the way I ground it out.

“Emotionally it was tougher pre-round yesterday. Today I was better pre-round but emotionally I got in a better space yesterday than today. Weird. Just to do with the start.

“Three was the killer for me. I hit a lovely swing down three and I just got a little stymied on the corner there and made four. You know five I missed it in the heavy stuff by a yard. Missed the correct side. Hit an okay pitch but left it on the wrong side of the hole.

“Made a bad swing off the tee on six. But I am in the semi and hit it in the left trap where you are supposed to hit it. Walking off six three over, then I hit a fantastic pitch shot to seven and missed that and at that point I was beginning to panic and saying, nothing is happening, what’s going on. T

“hen I get a jumper from the right semi on nine and my world was starting to collapse. To turn it back from there was good.”