Riordan was signed in June 2006 after scoring 64 goals in 146 appearances for Hibernian but has failed to make an impact at Parkhead.
The 25-year-old could not even find a place on the bench for Saturday's 1-0 defeat by Motherwell which all but ended their Clydesdale Bank Premier League title hopes.
"I only get chucked on when we need a goal so he must think I can get him one," Riordan told Scotland on Sunday.
"But he obviously doesn't want to do it unless he really has to because he doesn't want me to prove him wrong.
"He knows I would score quite a lot if he played me as much as he has played the other strikers but I don't think he wants to be proved wrong.
"When I speak to him, he's nice to me and says all the things that players want to hear about me being part of his plans but you know by his actions that he is talking rubbish.
"It is frustrating. I was left out of the squad (for the defeat against Motherwell) and was training with the reserves on Friday.
"I've virtually chucked it at Celtic, what's the point when I'm not getting a chance?
"I feel let down by the manager. I remember him sitting in my mum's house trying to sign me and he said I could play anywhere in his midfield or up front.
"It was the same in the press conferences but now I can only play left-midfield for some reason and that's not even my best position."