Murray was hoping for an extended run on home grass as he continued his build-up to his Grand Slam comeback at Wimbledon.
But those hopes were ended in a straight-sets defeat to Italy’s world number nine as Murray lost out 6-3, 6-3.
The Scot picked up his first singles victory in three months earlier in the week when he defeated Benoit Paire.
But Murray was unable to build on that momentum against Berrettini, who proved to be a much tougher test.
Murray’s defeat deprived British tennis fans the chance to see an all-British quarter-final between Murray and Dan Evans, who defeated France’s Adrian Mannarino to book his place in the last eight.
Now Evans will face Berrettini looking to earn a spot in the semi-finals.
“There are some slight niggles in the groin and I will have to try and get rid of that between now and Wimbledon,” he explained.
“I need matches and I need to practice with top players over the next 10 days.”