City are scheduled to fly out to Greece at Monday lunchtime ahead of this first-leg match.
Hart is already set for the next challenge after Wayne Rooney's wonder goal gave Manchester United a 2-1 victory at Old Trafford on Saturday.
Hart stopper: The England goalkeeper expects Manchester City to bounce back from their derby defeat to rivals United with a Europa League win
City midfielder David Silva cancelled out Nani's opener, only for the England striker to have the last word.
Hart said: 'It's deflated us a bit, but you've got to pick yourselves up and move on.
'You can't give up. If you're going to do that then there's no point in turning up every week. We are here to win games, do well for Manchester City and push the club on. That's not changed.
'We are still in the hunt for trophies, and we want to make it happen. The derby has gone.
'It's unfortunate that we lost, but we have to brush ourselves down and carry on. We've got the Europa League and the FA Cup as well as the Premier League to focus on.
Stealing the show: Hart was left bitterly disappointed but left with no chance to prevent Wayne Rooney's incredible match-winner at Old Trafford
'We know what we are about. People have been talking about Manchester United all season, but we played well. It's just a shame that we couldn't produce that bit of magic.'
England goalkeeper Hart had no chance with Rooney's overhead kick winner and added on his club`s official website: 'I think you've got to admire skill like that, it's just a shame that it was against us.
'It's what he's capable of, and it's probably been bottled up for the whole season. He's summed himself up as a player and also shut a few critics up with that strike.'
Midfielder Nigel de Jong looks set to miss the last-32 encounter as he remains troubled with an ankle injury while striker Mario Balotelli is expected to return on Sunday against Notts County in an FA Cup replay following an knee problem.
Aris are protecting a 40-year unbeaten run in European competition, spanning 24 matches, at their Kleanthis Vikelidis Stadium.
Greece is the word: City travel to Greece to take on Aris, and star Michel Garbino-Pereira (R)
However caretaker-coach Ioannis Michalitsios, who played for the club, fears the worst.
He said: 'Manchester City are a powerhouse. Emmanuel Adebayor was on the bench and now he is a first-team player on loan at Real Madrid.
'There is no secret to Aris's home success. It's a record that spans four decades and many generations of players. The common factor is the fans.
'Our supporters transmit their energy to the players - they can lift them when they are feeling down, they sing non-stop for two hours, it's impressive.'
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Explore more:People: Joe Hart, Wayne Rooney, David Silva, Emmanuel Adebayor, Mario Balotelli, Nani Places: Greece, United Kingdom