Rose, who had three bogeys and one birdie in a typically gutsy 73, gave a huge fist pump after holing a six-footer for par at the last.
“I found it really hard to enjoy the day,” said the 43-year-old, who won the 2013 US Open and 2016 Olympic title.
“I felt like it was good energy from the crowd, but with everyone with umbrellas up, no one is clapping; everyone is more shouting and cheering, wanting high fives.
“I normally engage in that type of stuff; today I just had my head down. I was not interested in anything. I was just trying to get around the golf course and hang in there.
“So to be able to go and have a moment on 18 where I could just let it out a little bit, just to show that I am super excited about the support, was big because until that point I was just grinding.”
World number 272 Brown has defied odds and expectation since leading on day one. And he looked poised to lead into the final round when he birdied the par-five 16th to get to six under.
However, the 2016 English Amateur champion bogeyed the par-three 17th after finding a bunker off the tee and then hit a six at the par-four last to drop from leader by one, to in the chasing pack.
“It was a bit of a sting on the last two holes through not really hitting a bad golf shot,” he said.
“Links golf got the better of me but we’re still there.
“I’m a little bit disappointed because I did so well so get to where I got to, and it’s a bit nasty to finish like that.
“But if you’d have told me I was going to go into the final round of the Open one or two shots back, I would have ripped your hand off.”
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