The 22-time Grand Slam title winner, back on court this week after three months on the sidelines, battled well but eventually crumbled against the hard-working world number 11 from Australia.
Nadal, 37, who missed virtually all of the 2023 season, is hoping to compete at the French Open in May where he is the record 14-time champion.
"On a personal level, for what is to come, the 6-1 in the second set is what had to happen today," said Nadal, who explained he did not want to push himself too far.
"That's the way I need to proceed today, to give me a chance to compete at Roland Garros," he added.
"I'll try to take a step further in Madrid, then in Rome, and if, in any tournament it's worth going out there to give everything and die, it's in Paris."
The Spaniard, who has won the Barcelona clay-court title on 12 occasions, had eased past Flavio Cobolli on Tuesday in his first ATP Tour match since January, but said he was not favourite against De Minaur who has now won his last two clashes against the former world number one.
It proved a far tougher challenge and despite showing flashes of his supreme quality on the court named after him, Nadal came up short in what he said he believes is his final appearance at the tournament.
The Australian broke in the first game and tested Nadal with a series of brilliant drop shots which Nadal could not reach.
However Nadal hit back with a break of his own in the sixth game and consolidated with a fizzing backhand for a 4-3 lead.
De Minaur broke to love to take a 6-5 lead as Nadal went wide and sealed the first set when the Spaniard pushed a shot into the net, winning the final 10 points as Nadal started to struggle.
The 25-year-old Australian broke for a 2-1 lead in the second set when Nadal could not return a powerful passing shot, and secured another break for 4-1.
De Minaur wrapped up his emphatic second set performance with a third break when Nadal went long.
It marked what Nadal said was "realistically" his final appearance at a tournament he loves.
"I had the chance to say goodbye here on court and that means a lot for me," he added.
"A week ago I felt I was not able to play any more at this event, that would be painful, but at least I played and now it's the moment to keep going."
Monte Carlo Masters champion Stefanos Tsitsipas faces Sebastian Ofner later Wednesday in the second round.
