Barton, who had a short spell at Ibrox club Rangers last season, has pointed out Celtic’s disappointing record in the Champions League under manager Brendan Rodgers.
The Hoops are playing in the group stage of the Champions League for the second season in a row.
However, the Glasgow giants have failed to progress to the knockout rounds, although they could end up in the Europa League this campaign.
Celtic were hammered 7-1 by Paris Saint-Germain in Paris in the Champions League last week, but the Bhoys recovered to get the better of Motherwell in the final of the Scottish League Cup at the weekend.
Former Rangers and QPR midfielder Barton believes that Celtic are flat-track bullies.
The former Newcastle United midfielder has also claimed that Neil Lennon showed more tactical nous in Europe with Celtic than Rodgers has.
Lennon, who is now the manager of Hibernian, was in the charge of the Hoops from 2010 until 2014.
"Getting beat 7-1 is amateur,” The Daily Record quotes Barton as saying. “It just gives people in England who have a lot of disrespect for the Scottish league, who don't think it's got any credibility and gives them all the ammo they need to say look how poor you are, that you get battered whenever you run into a decent side and that Celtic are flat-track bullies.”
"Everyone's going about Brendan, how good Brendan is,” added Barton. “Listen you can't knock them domestically, but I just think in Europe, Neil Lennon showed a bit more tactical nous.
"Celtic never got humped and that's the only way to describe what happened in the Parc Des Princes during the week. Celtic have to adjust from the domestic campaign to cut their cloth accordingly."