Guardiola made the admission during a discussion marking former sporting director Txiki Begiristain's departure from City.
Guardiola admitted that he made one of his "biggest mistakes" while at City. He was surprised when he named a player who should have stayed with the team longer.
"I'll choose a less obvious name: Jesus Navas. He should have stayed with us longer, " said the Catalan manager, who shared just one season with the Spanish full-back.
In four seasons, Navas made 183 appearances, scoring eight goals and providing 35 assists for City.
"Thank you for the gift of spending a year together, and how I regret letting you go. I would have loved it if you had stayed longer, but sometimes you make mistakes," said Guardiola.
On Guardiola's most important player at City, he added: "Gundogan, because he was of great value to us. I choose him."