The 33-year-old, now ranked 123rd after a series of hip and groin injuries, lost 7-5, 6-2 to in-form Russian Andrey Rublev on Wednesday.
It was always going to be a tough ask against the world number eight, with Murray having lost in the first round of his first ATP event since October in Montpellier last week.
“I want to be playing at this level because I learn a lot from a match like tonight,” Murray told atptour.com.
“The issues and the mistakes that you make get amplified more at this level…
“I do feel tonight there were some good, positive signs there. Just when it mattered, I wasn’t good enough. I will need to improve.”
A high-quality opening set against Rublev, who has played in the last eight of Grand Slam tournaments four times since Murray’s last major quarter-final in 2017, was a far cry from the second-tier Challenger tournament in Italy where the Briton kicked off his 2021 season.
The three-time Grand Slam champion missed the Australian Open after testing positive for coronavirus.
Roger Federer is also set to make his comeback from a lengthy spell on the sidelines next week in Doha, and Murray backed his old rival to find his rhythm quickly.
“I just want to get out and compete and just enjoy doing what I am doing. I imagine Roger would be the same,” added Murray.
“I am sure he has been training hard and is excited to get back out there and compete.
“I am sure in time, providing that his body is good, that he will play top-level tennis again because he is that good. Even if there is a slight drop-off physically for him, I would back his skill against most players.
“I am sure he will be fine.”
Federer has not played since losing to Novak Djokovic in the semi-finals of last year’s Australian Open.
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