The three-time Grand Slam champion played just seven matches in a disrupted 2020 season, due to a series of niggling injuries and the coronavirus pandemic.
“Every time I lose a match I’m getting told to retire, that I should stop playing, that I’m finished and I’ve got nothing left,” said Murray after beating Haase.
“There’s a bit of extra doubt there. And on top of that I’m playing with a metal hip, which is hard.
“It’s a big challenge for me just now and one that I will meet head on, but it’s not easy.”
Murray showed all of his fighting qualities to see off Haase, who is ranked 193rd in the world, in a 2-6 7-6 (7-2) 6-3 victory lasting two-and-a-half hours.
Murray struggled in the opening set as Haase hit confidently and cleanly, but the Scot improved – helped by loudly geeing himself up and even thumping himself on the forehead – to turn the match around.
He played a superb tie-break to win the second and then, after trailing 3-0 in the decider, upped his level again to win six games in a row and seal victory.
“I was really struggling with my game for probably an hour and a half,” said Murray, who was given a wildcard to play in Rotterdam.
“I was mistiming the ball, it was very strange, I didn’t quite know what to do out there. And then I found a way and at the end actually started to play a bit better.
“The physical side was positive, I played for two and a half hours, and my hips and groin felt good. But tennis side – it was average, at best.”
Russian fourth seed Andrey Rublev could be Murray’s next opponent and faces American Marcos Giron on Tuesday for the right to face the Briton in the second round.
Earlier on Monday, British number three Cameron Norrie continued his decent start to the 2021 season with a dominant first-round win over Georgia’s Nikoloz Basilashvili.
The 25-year-old won the first seven games of the match against 40th-ranked Basilashvili, going on to wrap up a 6-0 6-3 victory in little over an hour.
Norrie, who came through qualifying, will play Switzerland’s Stan Wawrinka or Russia’s Karen Khachanov next.