Pedro Caixinha's new-look Rangers were knocked out of Europe by Progres Niederkorn on Tuesday.
Barton signed for Rangers during last summer's transfer window, but left in acrimonious circumstances after only eight appearances for the Ibrox side.
The manager who signed Barton, Mark Warburton, has since been replaced by Pedro Caixinha, who has utilised contacts in Mexico and his native Portugal to overhaul a Rangers squad which struggled in its first season back in Scotland's top flight.
Rangers manager Pedro Caixinha
Of Rangers' eight summer signings so far, only Ryan Jack has any prior experience of British football, although he could soon be joined at Ibrox by Graham Dorrans of Norwich City.
While it is still early days, Caixinha's new look side appear to have made little progress since last season, and were dumped out of the Europa League by Luxembourg's fourth best team on Tuesday.
Discussing the result with Talksport's Jim White this morning [Wednesday], Barton said: "The worrying thing for me would be I see the likes of Andy Halliday leaving the football club, it looks like Barrie McKay is going to leave the football club.
"What I gathered in the time I was there is these are people who know the football club, certainly in Andy’s case.
"I’m not saying he would have made a huge difference but he’s someone who cares deeply about the club, he’s a supporter, he’s a fan, he’s somebody who has got the club running through the ethos of his family. I want to see people like that."
Rangers-owned midfielder Andy Halliday [centre]
Barton's contract was finally terminated two months later, and he is currently without a club due to a ban imposed playing for Burnley earlier this year.
Is Barton right about Rangers' transfer policy?
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