Alvarez moved to Atletico in an £81 million ($106 million) deal earlier in August after Guardiola accepted his wish to leave in search of more regular playing time.
Erling Haaland is well established as City's first-choice striker but Guardiola had initially hoped to replace Alvarez to ensure there was sufficient depth behind the Norway star.
The Premier League champions were linked with FC Copenhagen's Orri Oskarsson and Celtic's Kyogo Furuhashi, but neither deal had come to fruition in the final hours before the transfer window shuts on Friday evening.
"I'm happy with the squad. We didn't expect Julian to leave, although he had conversations a long time ago with other clubs and his agent, so it could happen and in the end it happened," Guardiola told reporters on Friday.
"We saw what we have, if we have many injuries it will be a problem, but in a few months Oscar Bobb will be back (from injury) and Phil (Foden) is in that position, McAtee can play in that position, Gundogan can play in that position.
"They are different players to Erling of course. Maybe it is a mistake, I don't know but I don't like leaving players without playing for a long time."
In keeping with Guardiola's preference for a small squad, German midfielder Ilkay Gundogan's return to the club from Barcelona and the signing of Brazilian forward Savinho from Troyes have been City's only close-season deals.
'All together'
James McAtee has also rejoined City after spending the last two seasons on loan at Sheffield United.
"When everyone is involved with a chance to play the performance of the teams is always better," Guardiola said.
"In winter, we have another chance (to sign players). If I'm not convinced, it's better to stay that way."
Savinho has made an immediate impact for City, providing his first assist for Kevin De Bruyne's goal in the win over Ipswich last weekend, while Gundogan came off the bench to make his second City debut.
After one season at Barcelona, Guardiola said the 33-year-old has slotted in as though he had never been away from Manchester.
"He needs one minute, no more than that to settle," Guardiola said. "Everybody knows it, he's a top class player. He knows the mechanics of what we try to do, what we try to live all together and he does it."
Guardiola is hoping for reinforcements for Saturday's Premier League trip to West Ham, with Rodri back in training and Mateo Kovacic recovering from a knee injury.
England forward Foden is expected to miss out again through illness.
Foden was included in Lee Carsley's first England squad on Thursday along with Rico Lewis, John Stones and Jack Grealish, but there was no place for Kyle Walker, who is yet to feature for City this season.
"He will be back to his best and it will be soon," Guardiola said of Walker. "Always he's an incredible weapon for the national team to use because he has specific qualities.
"He was late back (after Euro 2024) and arrived with a few niggles."
