The midfielder’s spot-kick was saved by goalkeeper Yassine Bounou as the 2010 World Cup winners failed to score any of their penalties.
“It was a pity. It was decided on penalties in the most cruel way,” said Busquets.
“It was tough, very hard for us. We tried to wear them down, give them the run-around, find spaces. We lacked that little luck for the final ball.”
Spain were also knocked out of Euro 2020 on penalties in the semi-finals by Italy.
Busquets, 34, would not be immediately drawn on whether he would continue playing international football.
“Now the most important thing is the national team and not me,” said the Barcelona player.
“It’s a tough night and we have to pick ourselves up and use this as experience for our game. There are some very young players who this will help a lot.”
Spain goalkeeper Unai Simon was the hero in Euro 2020 against Switzerland in a quarter-final shoot-out but on this occasion he could only stop one of Morocco’s efforts.
“I think in the 120 minutes of the game we were superior to our opponents, but what I say counts for little now if we can’t find the net,” added Simon, who saved Badr Benoun’s penalty.
“In the shoot-out they were superior and that is what took them to the quarter-finals.
“We are seeing that there are surprises throughout the World Cup. We were not capable of overcoming them and we did not expect to be eliminated against Morocco, but it’s the reality and now we have to go home.”
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