The back-to-back Premier League winners have been hit with a two-year suspension from European competition by governing body UEFA over Financial Fair Play rule breaches.
The club are appealing to the Court of Arbitration for Sport but, as things stand, City will play only in domestic football in 2020-21 and 2021-22.
Fleetwood manager Barton, 37, who was a trainee at City and spent four years in the first team, said: "I don't know the ins and outs of it, and if I'm totally honest I don't particularly care about it, but I don't like the thought of seeing City not in the Champions League.
"They are one of the best sides in our country, so it's a strange one because when that size of a club, with that level of a manager and players...you have to be in Europe's major competition.
"For English football you want your best teams in that competition."
The ban has sparked speculation about the future of City manager Pep Guardiola and some of their star players. There are also fears it could hamper their ability to recruit their top targets in the transfer market.
Barton's former team-mate Jon Macken, however, is confident the club will still be able to punch their weight on and off the field.
Macken, 42, who played for City from 2002-05, told the PA news agency: "Everyone says they might not stay but this is Manchester City, a fantastic football club.
"Manchester City are a global success story. Everyone wants to come to Manchester City because of how successful they are and because they have arguably got the greatest manager.
"I know they are not going to be in the Champions League – which is the best competition in the world – but still the Premier League, FA Cup and League Cup will be a big attraction for many, many players.
"It's up to them. I suppose you will get players who will want to play Champions League but they should be looking at the bigger picture – what Manchester City bring as a whole, not in the short term but in the long term.
"When you attract someone like Pep, with his profile, there is always the worry that he might go on to other things but, at the end of the day, Manchester City are massive global attraction for anybody – any manager, any player, fans."
Former City defender Keith Curle, who is now the manager of League Two Northampton, believes City have got a good case for an appeal.
The 56-year-old said: "I think they have grounds to appeal. I'm sure if they feel they have been wronged then they will fight that case.
"It's a massive thing for them because they need to attract the best players in the world to that football club."
Ex-City skipper Andy Morrison is confident the club will ride the storm.
The manager of Welsh side Connah's Quay tweeted: "There are times in life where you have to take a deep breath, put your faith in the system and trust the process.
"This is an opportunity for the Owners, Manager, Players and fans to UNITE yet again as one. The most successful club of the last decade ain't going anywhere."
Barton, however, did cheekily add that he saw one positive.
If City's ban is upheld, fifth place in the Premier League will qualify for next year's Champions League.
The Fleetwood manager, who grew up an Everton fan, said: "It'll certainly make the race for fifth place more exciting, particularly for me as an Evertonian!"