Towering striker Smith made his name under Dickov at Oldham last term by scoring against Liverpool and Everton and, after a summer switch, he registered his first Leeds goal on Tuesday night.
Smith restored United's lead just 15 minutes after Doncaster had equalised in a pivotal moment of the game, but Dickov claimed it should not have been allowed as the 6ft 6in frontman was climbing all over defender Bongani Khumalo.
Yet Whites boss McDermott said: "I didn't think it was a foul when Matt Smith scored. I thought it was a good header and he was a real handful for them all night.
"Whether Matt's goal was contentious or not I thought he challenged for the ball fairly and he's a strong lad in the air. In any case we had a complaint before they scored because (Alex) Mowatt was fouled on the edge of the box before they gained possession."
He added: "I thought Doncaster played well for the first 20 minutes but once we got amongst them I thought we were in control.
"It was a good first goal but we allowed them back into the game before we managed to clinch the tie.
"I gave Mowatt his debut and he showed he can play a part this season because it won't phase him playing at home or away.
"Neil Redfearn has done a great job with the younger players and we should be proud of our Academy."