McNamara's men recovered from conceding an early goal to go 2-1 up and Jon Daly then scored his second goal of the game to make it 3-3, after Celtic had surged into a 3-2 lead.
But it was the Bhoys who will advance to face Hibernian in the final, after Anthony Stokes headed home a James Forrest cross in extra time.
McNamara said: "Disappointed to lose but I couldn't have asked for any more and I'm proud of the lads today, they gave us everything.
"I thought the players were exceptional, every one of them. They gave everything they had and caused Celtic problems."
McNamara felt that Celtic's third goal, a second for Kris Commons, could have been ruled out for handball, and that his side should have had a penalty when Gary Mackay-Steven tangled with Victor Wanyama.
"I thought Gary got his body in the right position," said McNamara. "And their second goal was a bit dubious.
"It hit Commons on the hand, although he maybe didn't know much about it. But, again, there is no point in crying about it."