On Friday, UEFA announced the Citizens will face a two-season ban from the Champions League and Europa League for committing breaches of the UEFA Club Licensing and Financial Fair Play Regulations.
City released a statement insisting they would appeal the punishment at the Court of Arbitration for Sport 'at the earlier opportunity'.
Arteta, who spent three-and-a-half years on Pep Guardiola's coaching staff before leaving to take up a managerial role with Arsenal in December, sympathises with his former club.
He told talkSPORT: "They have all my sympathy because I love them so much. I'm so grateful for them, for everything they did with me and the time we spent together.
"I suffer because I know they are going through a difficult time. They have my full support and I'm right behind them.
"At the start, I was very shocked. My first reaction was to try to speak to them to see how they were feeling. We'll see what happens."
If City's appeal fails and they finish in a top four position this season, fifth spot will reportedly earn a club Champions League football for the 2020/21 campaign.
Following Arsenal's 4-0 win over Newcastle on Sunday, Arteta's men are just six points behind fifth-placed Tottenham.
When asked about qualifying for the Champions League, Arteta said: "Honestly, I'm just aiming to improve this process, performing better, playing better and that will lead to results.
"If we are able to sustain that, I'm convinced in the last three of four games of the season, we're going to have a chance.
"If we don't do that, it doesn't matter if it's fourth or fifth [to qualify], we'll have no chance."
Mikel Arteta insists Man City have his full support in the wake of their European football ban.