Cleverley was part of the Team GB squad which reached the quarterfinals.
"The way sport was showcased in the Olympics was an example for everyone in every sport; the sportsmanship, the respect we had for everyone," said 23-year-old Manchester United midfielder Cleverley.
"It was unbelievable, something I look back on, even now, as being just amazing. I got to speak to other athletes from different sports.
"I spoke to Anthony Ogogo, the boxer. He's a United fan and I was asking him when his fights were, how long he'd been training and whether he gets nervous.
"Every Team GB athlete warmed up in the same gym and you'd be looking at them wondering which sport they were from, doing a warm-up like that."