Six-foot-six Smith made his name at under Dickov at Oldham by scoring against Liverpool and Everton, but registered his first Leeds goal on Tuesday as the Whites beat Rovers 3-1 in the Capital One Cup.
Smith restored United's lead just 15 minutes after Doncaster had equalised in a pivotal moment of the game.
But Dickov, who gave Smith his professional break, said: "Matt's goal changed the match and in my opinion it shouldn't have been allowed.
"He had his hands on our centre half's shoulders and held him down when he headed in. I've seen it back on the video and it's a clear foul.
"I signed Matt from non-league and gave him his professional debut so I know what a threat he can be.
"It's disappointing to lose the game because we started very well on the front foot and caused them a lot of problems.
"The first goal we conceded was disappointing from our point of view because we allowed them the first header and then the second touch.
"We were back in the match when we equalised and the penalty was irrelevant because we were pushing forward at that stage to try to get back in the game.
"Although the result was disappointing there were positives to come out of the game for us. Billy Paynter scored his first goal of the season after coming on as substitute and his attitude has been first class while he's been waiting for his chance.
"But we are out of the competition now and that's disappointing from a financial point of view as well as everything else."
Leeds manager Brian McDermott was pleased with the performance and said: "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 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.
"I gave Alex Mowatt his debut tonight 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.
"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 Mowatt was fouled on the edge of the box before they gained possession."