But there was a much better outing for Alexei Popyrin, who has the tools and form to spring a surprise at the London grand slam, and enjoyed a very useful work-out in beating compatriot Aleksandar Vukic in three sets.
There was also a shock main court appearance for Adam Walton, who was suddenly called up to face world No.2 Carlos Alcaraz as a lucky loser. That was because Alejandro Davidovich Fokina - who had come to England after getting married in Marbella, Spain, at the weekend - had withdrawn with illness.
Walton, ranked 86, lost 6-4 7-6 (7-4) but acquitted himself well in his main draw Queen's debut under a blazing sun on Andy Murray Arena.
In the first set he held serve easily to 3-3, but was then broken in his fourth service game after saving several break points, to give Alcaraz a lead he did not relinquish.
But Alcaraz, the 2023 Queen's winner who will soon be bidding for a third successive Wimbledon title, was unable to break Walton in the second set and needed the tiebreak to take the set, and match.
Alcaraz had been practising with another Aussie, Jordan Thompson, when he was given the news, which he greeted with a grin towards Thompson..
But Thompson was not smiling later on Tuesday as he was forced to retire when playing Jaume Munar. Munar will now play Alcaraz in an all-Spanish clash.
It was not immediately clear why Thompson, a semi-finalist last year, retired after losing the first set 7-5, but with Wimbledon imminent it may have been precautionary.
De Minaur was playing his first match on grass this year, and his first on any surface since tumbling out of Roland Garros in the first week.
He had taken a break to reset, professing mental and physical burn-out, but looked flat on court as he lost 6-4 6-2 to powerful world No.30 Jiri Lehecka.
De Minaur was broken in the opening game, and never managed to break back in the first set as Lehecka served up to 226kph. He was unable to break in the second set either, dropping serve himself at 1-1, in part due to an unlucky netcord, and 2-4.
"There's not too many positives I can take out of today. Just not a good day at the office - I wasn't up for the level," said de Minaur.
"If you want to be effective against him, you've got to be ready from the very first point till the last and you need to bring a high level. Today I did not do that.
Forehand errors and a poor first serve were de Minaur's main failings, though Lehecka played well too.
"We all know how well Alex can play on grass, I knew I needed to serve well and be aggressive," said the Czech. "The first game was very important, to be a break up was a great advantage."
It was the first time Lehecka had beaten a top-12 ranked player on grass.
Popyrin, now ranked 21, took the first set against Vukic easily enough but was then drawn into a dogfight which will prove useful for both players, eventually winning 6-2 6-7 (9-11) 7-6 (7-3).
Popyrin will now play Jack Draper, the British No.1 and No.2 seed, who dismissed Jenson Brooksby 6-3 6-1.
American sixth seed Ben Shelton, who had reached the semi-finals in Stuttgart last week, was knocked out in a 7-6 (7-5) 7-6 (7-4) loss to French qualifier Arthur Rinderknech.
7°C