Hoops’ striker Georgios Samaras put the visitors into the lead five minutes from the break when he headed an Andreas Hinkel cross past the helpless Hibs keeper Graham Stack.
However, the game’s most controversial moment arrived in the 62nd minute when Republic of Ireland international McGeady, booked in the first half for a foul on Derek Riordan, picked up a second caution from referee Dougie McDonald for taking a dive in a touchline challenge with Hibs defender Paul Hanlon.
The decision was made more significant given that it came at the end of a week in which Celtic had been victim of a diving incident involving Arsenal player Eduardo, who won and scored a controversial penalty during the Champions League play-off match at the Emirates on Wednesday.
Mowbray, who refused to look at the McGeady incident again on television afterwards, believed it was the furore surrounding Eduardo which led to McDonald taking action.
The Celtic boss fumed: “If the Eduardo situation had not been blown up so big nationally, 99 times out of 100, maybe even 100 out of 100, it would never have been a yellow card.
“I think the referee has been influenced by the diving situation.
“I don’t need to look at it again, it happened right in front of me.
“It was unfortunate for Aiden. It was a poor decision and we are in all in disbelief. You have to put it into the context of the boy travelling 50 yards before the incident. He went to ground because he was knackered.
“Is it a dive? Never in a million years. A dive is when you try to influence the referee, you throw your arms up and so on.”
Mowbray, who denied that he was aware of interest in Scott Brown, Scott McDonald and McGeady, all of whom have been linked with various clubs in recent weeks, insists the assistant referee had actually flagged for a Celtic free-kick.
“I am not going to criticise the officials but the linesman flagged for a foul for us,” he said.
Hibs manager John Hughes was reluctant to get involved in the McGeady debate.
He said: “You never wanted to see an opposition player sent off, especially Aiden, you want to see his class. To tell you the truth I thought at first that Hanlon was getting booked.”
Meanwhile Rangers notched up their third successive win.
The champions romped to a comfortable 4-1 win over Hamilton at Ibrox with both Whittaker and Kris Boyd helping themselves to two goals each.
The win followed victories over Falkirk and Hearts and ensured Rangers remain at the summit of the Premier League.
HIBERNIAN: Stack, McCormack (Byrne 67), Bamba, Hogg, Hanlon, Wotherspoon, Cregg (Zemmama 61), McBride, Rankin, Stokes (Nish 76), Riordan.
CELTIC: Boruc, Hinkel, Caldwell, Loovens, Daniel Fox, Maloney (Flood 69), Scott Brown, N’Guemo (Caddis 78), McGeady, Samaras, McDonald (Killen 69).
Ref: D McDonald.