Westwood, who is the leading British player, is currently five shots off the lead at Augusta.
He was disappointed that he could finish with a better score in the end after hitting the ball pretty well throughout Saturday.
"It was hard work out there," Westwood told BBC Sport. "It was tricky.
"The greens are firmer, as they always are on the weekend. I could've shot under par though.
"I was hitting the ball well, eight and 13, and right down the middle on 15 but still couldn't make birdie. I rolled a 70 into a 73 but I've still got a good chance."