While Murray said his hip injury was not to blame for his exit, three-time Wimbledon champion Becker told the BBC the Briton's movement was clearly affected.
"He has got to think long term, not worry about making the U.S. Open - if he is moving there like he did at Wimbledon, then he won't win it anyway," the German said.
"His ranking should not be a concern either. Again, he will not defend it if he is not healthy, so he should just forget it. He has been there and done it and he does not have to prove anything anymore that he is good enough to be number one."
Becker said he understood why Murray would have played at Wimbledon even if he was not 100 percent fit.
"I understand why Andy played Wimbledon, because it is his number one tournament every year, and he was also the defending champion. He was desperate to make it work," added Becker, who won six grand slam titles.
"I was always the same. In hindsight, I should not have played some of my matches but, in the heat of the moment, I always wanted to play the next round or the next event... But you run the risk of doing yourself more serious damage if you play on.
Becker said Murray should take some time to evaluate his fitness.
"Andy is now at the point where he needs to be really honest with himself because if he can't run, he can't play.
"I credit him for not wanting to use the hip injury as an excuse for his defeat but he needs to get a couple of opinions from doctors before he thinks about coming back."
The U.S. Open, the final grand slam of the year, begins on Aug. 28.
(Reporting by Aditi Prakash in Bengaluru; Editing by Peter Rutherford)
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