Mahan lost a Ryder Cup singles match to Graeme McDowell at Celtic Manor in 2010 when he duffed a chip shot to the 17th green and conceded a victory which handed the trophy to Europe.
"I don't need any redemption or anything like that, just playing golf," the 31-year-old told reporters after finishing two behind Westwood on 212, one under.
"I don't play golf for revenge or to make up for anything. I'm playing because I really like to play and it's the ultimate challenge playing major golf. So that's the only thing I'm worried about."
Mahan, who finished tied fourth at last month's U.S. Open, shot 72 in his first two rounds at Muirfield but five birdies sent him shooting up a congested leader board on another testing day at the East Lothian links.
"Obviously the course is difficult," he said. "I don't know how many guys are under par right now. Any score in the red is good. I played really solid today tee to green. Just two bogeys.
"But I hit a lot of good quality shots and the putter was obviously very strong, making a bomb on two and a bunch of key putts coming in. It was a total team effort by my game today."
Mahan was honest enough to admit his game may not have been good enough to win majors in the past.
"Probably my short game hasn't been as strong as it needed to be," he said. "But I'm chipping and putting great and doing all the right things.
"So I feel comfortable with my game and excited about the opportunity and just have to go out there and trust it and let it happen."
(Editing by Tony Jimenez)
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