This was the first-high profile game for McCurry since he was accused of bias by Dundee United manager Craig Levein after the Tannadice side had lost against Rangers at Ibrox last May.
There was no doubt about the first penalty awarded to Celtic when Shaun Maloney was brought down by Garry Hay and although the former Aston Villa player missed the target with his spot-kick, he struck soon after to give the visitors a half-time lead.
When Georgios Samaras scored 10 minutes after the break the points were safe but Combe was raging at the second penalty awarded by McCurry 10 minutes from the end, when Shunsuke Nakamura – who converted the spot-kick – was adjudged to have been pulled back by Craig Bryson.
Samaras scored from the spot before Killie midfielder Mehdi Taouil scored a consolation from the spot after Celtic defender Gary Caldwell was dismissed for handling the ball on the line.
Combe had no complaints about the result but had little good to say about Shunsuke Nakamura or McCurry.
He said: “There were 11 players on that pitch and 5,000 Killie fans who were upset by that because it was never a penalty.
“The fact Nakamura got up with the biggest grin on his face tells a story. He went down too easy, without a doubt.
“In saying that, they were 2-0 up at the time and we were never in the game — but losing three goals was disappointing.
“It was a soft penalty we got against us at Ibrox last week.
“You could see with the abuse he was getting with all the singing, maybe that played on his (McCurry’s) mind, I don’t know.”
Kilmarnock manager Jim Jefferies agreed with Combe’s overall assessment.
“We’ve been told that television monitors showed that it definitely wasn’t a penalty.
“It was a difficult situation for him (McCurry). If he had given a lot our way that may have caused a stir.
“But I’m not looking for an excuse for my team, we deserved to lose the game.”
Strachan backed Nakamura saying, “We had some good performances and I think Nakamura was phenomenal again.
“If anybody was watching on the telly to tell their kids how to play football, that’s the way to play football.
“But I would be unhappy if I thought Nakamura was taking a penalty against me.”
Combe, Fowler, Wright, Ford, Hay (Hamill 71), Pascali, Bryson, Skelton (Sammon 31), Invincibile, Fernandez (Simmonds 71), Taouil.
Boruc, Wilson, McManus, Caldwell, Naylor, Scott Brown, Crosas (Hartley 74), Nakamura, Maloney (McGeady 61), Samaras, Vennegoor of Hesselink (Loovens 90).