Three-time major winner Padraig Harrington has not given up hope of qualifying for the US Open, despite missing out in Monday's qualifying event at Walton Heath.

Harrington bogeyed the final hole to finish one shot outside a play-off for the remaining four places at Chambers Bay next month, but can still qualify via the world rankings published in the week of the year’s second major.

“I believe that the top 60 after the St Jude Classic (in Memphis) still get into the US Open,” said Harrington, who is currently ranked 86th. “So I have this week’s Irish Open and the St Jude Classic. I won’t play the one in between. I’m already on a run of four events.

“I have to win 25 world ranking points in that time, something like that. I certainly think a win here or at St Jude will push me across the line, or some sort of combination (of results).

“Having missed out yesterday it was very disappointing, but it will be a lot more disappointing in three weeks’ time when I’m sitting on the couch watching it on TV and realising how close it was and really having done all the hard work.”

Harrington played the 36-hole qualifying event despite having lasted just two holes of the BMW PGA Championship at Wentworth with a shoulder injury, and the 2007 champion is confident the problem will not affect his participation in the Irish Open at Royal County Down.

“It’s certainly improved enough that I don’t feel like there’s any doubt about me playing on Thursday,” he added. “It’s not quite 100 per cent at the moment but I was pleased yesterday that as much as a hindrance it was early on, as I got into it more and more it was less of a problem.”