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Murray, a five-time champion at Queen's, was beaten 6-3 6-3 by Italian Berrettini as the three-time grand slam champion struggled a day on from being given a Wimbledon wildcard.
The former world number one beat Benoit Paire in his first ATP Tour singles match since March on Tuesday, but the 34-year-old revealed he is still being troubled by a groin injury after his loss to Berrettini and knows he must raise his game.
Murray said: "I actually felt my movement was actually quite good for both of the matches. My tennis today was not very good. That's the thing that I'll need to improve the most.
"Then there is still a slight niggle in the groin, so [I have] to try to get rid of that discomfort between now and Wimbledon. I need to be playing points, basically. I played two sets in preparation for this event.
"I do feel like I genuinely have been hitting the ball well in practice, but then like today when you're under a bit more pressure and stuff and you're having to make very split-second decisions when you're on the court, if the guy is serving 140 miles an hour, like, it's difficult to prepare for that."
Dan Evans made history earlier in the day, getting the better of Adrian Mannarino 6-4 7-6 (9-7).
With Jack Draper and Cameron Norrie having already progressed, Evans' win ensured there will be three Britons in the singles quarter-finals for the first time in the Open Era.
Feliciano Lopez will not retain his title in London after the Spaniard went down 6-2 6-3 to second seed Denis Shapovalov. Spanish veteran Lopez won in 2019, with last year's tournament cancelled due to the pandemic.
There will be no glory on home soil in Halle for German Zverev, who was taken out 7-6 (7-4) 3-6 6-3 by unseeded Frenchman Humbert.
Humbert has now beaten a top-10 player on every surface, with Zverev serving 20 aces but bowing out after his 22-year-old opponent claimed the only break of the final set.
Sebastian Korda battled past Kei Nishikori 2-6 6-3 7-5 in Halle, while Lloyd Harris also moved into the last eight at Lukas Lacko's expense.