City's 1-0 win over Steaua Bucharest on Wednesday sealed their place in the competition's group phase, but supporters used the game to voice dissent over Guardiola's treatment of Hart.
The England goalkeeper, who is due to be replaced by Barcelona's Claudio Bravo, was serenaded throughout, but Guardiola said he had been hired by City to make difficult decisions.
"I'm here to take decisions. I was honest with Joe, I was honest with the club, I was honest with all the players in the squad," said the Catalan, whose name was also chanted by City's fans.
"I have to take decisions and I can't deny what I feel. When the fans are unhappy, I can completely understand that.
"What Joe has made in this club is much more than I did in my past, which is just one month here, and I'm pretty sure what I will do with this club.
"Because there are a lot of players who are so important. Guys like Yaya (Toure), like Samir (Nasri), like David Silva, like Gael Clichy, like (Aleksandar) Kolarov make this club like this.
"This club has just once in their life gone more than the group stage, to the semi-finals. It was last year with Manuel (Pellegrini).
"So it's not a club for the European history. These guys who were here create this step and I respect (them) a lot. But I'm here and I have to take decisions.
"You can't think when I was in Barcelona, in (Bayern) Munich all my decisions were right. Time showed I made mistakes. But I have to take it.
"That's why Manchester City contacted me and asked me to be the new manager. I accepted. If I accept, you have to follow me. You have to play the way I want to play."
City's fans sang "Don't sell Joe Hart!" and "City's number one!", while a second-half chorus of "Stand up if you love Joe Hart!" drew almost the whole stadium to its feet.
Hart likened his situation to a "circus", but he stopped short of criticising Guardiola.
"We have a top manager that the club has wanted for a long, long time," said the England goalkeeper, who was making his first competitive appearance of the season.
"He will have his opinion on things and outside of the charade and all the rubbish that is being talked, we are dealing with it like men inside and we will come up with a solution.
"Tonight I played for Man City and I enjoyed it and I have done every time I have played for Man City."
Asked what the future held for him, Hart told BT Sport: "It's not for me to say. It is what it is." City's win, secured by a 56th-minute Fabian Delph header, completed a 6-0 aggregate victory.
They will discover their Champions League group-phase opponents in Thursday's draw in Monaco, while Steaua slip into the Europa League. "It was a beautiful experience for us," said Steaua coach Laurentiu Reghecampf.
"We have lots to learn. We have met one of the most powerful teams in Europe and I hope we will have a better route in the Europa League."
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