And he reckons fans will vote with their feet if the Hoops crash out of the Champions League qualifiers against Legia Warsaw tomorrow and lose more star players.
New boss Ronny Deila has so far only brought in keeper Craig Gordon - a free agent - and out-of-favour Cardiff midfielder Jo Inge Berget on loan this summer.
McAvennie said: "I'm worried about Celtic's season if they don't get past Legia Warsaw. If they don't overturn that 4-1 loss from the first leg I think they'll lose Virgil van Dijk and Fraser Forster. And I hear a few more want to leave.
"The fans will only take so much if the club is not investing. I know a lot of people who had hospitality boxes and season tickets at Celtic Park and they're not taking them out this year. Nobody is going to watch them if some of those players leave.
"I'm worried because this is not the Celtic I knew. I don't even know who Ronny Deila is."
Macca admitted it may make business sense to let English goalie Forster go. The Radio Clyde pundit said: "If Gordon is fit, he is a top-class keeper so if they get good money for Fraser they should take it.
"But Celtic don't have anyone to take Van Dijk's place. There's obviously nobody in the reserves or youth team because they played against Spurs and got battered."
However, McAvennie still thinks Celtic have a chance of turning round the tie against the Poles.
He explained: "If they can get the ball to Kris Commons and get Griffiths and Stokes playing, the Hoops have a chance.
"Legia scored four in the first leg, it could have been six or seven, but Celts have a better team so they can beat them."