The Argentine striker said publicly in June that he had discussed his future with the club and that "the best thing for everyone would be a transfer", adding that he was keen to fulfil his dream.
Barcelona President Joan Laporta confirmed in August that the club were interested in signing Alvarez, but Atletico refused to sell him in a transfer saga that dominated sports headlines in Spain over the summer.
"It feels a bit strange when a teammate says publicly that he wants to leave. It didn’t sit very well with us," Baena told the radio station Cadena SER on Monday night.
"I can understand a player having doubts if a club like Barca or Real Madrid comes in for you, but, ultimately, it was the way he went about it that really annoyed us at Atletico."
Alvarez apologised to Atletico fans in October for his comments and, while the intense whistling reserved for him at the Metropolitano at the start of the season has subsided, there is still audible hostility from the Atletico crowd.
"We would have supported him regardless of what he decided to do. The important thing is that he is with us now, and we need to show him all the affection in the world," said Baena.
Similarly, manager Diego Simeone told a press conference on Sunday that Atletico would wait for Alvarez to return to his best because "he's a great player and we love him".
Barcelona sporting director Deco confirmed in September that Barcelona had made an offer for Alvarez in the summer, but said that "Julian is in the past" as he looked to move on from the story.