Keith Watson headed the visitors in front, before Jon Daly and Willo Flood added others during the final 20 minutes.
However, Smith was annoyed that his own side were not awarded a penalty when they trailed 1-0 and that the visitors later netted their second goal from the spot.
The game appeared to swing on a controversial decision when Dundee were denied a spot-kick after Brian McLean had handled the ball.
Then United were awarded one themselves after referee Willie Collum played an advantage which ended with Daly failing to score following a foul by Gary Irvine on Stuart Armstrong.
Collum then blew his whistle giving Daly a second bite of the cherry to find the back of the net from 15 yards.
Smith said: "It's very disappointing, two major decisions have gone against us.
"There are too many grey areas where it's an easy option for referees.
"From where I was standing, he (McLean) moved his arm towards the ball. It's an unnatural position and it's a penalty but it's a grey area.
"The second is another grey area: Is there advantage, is there not advantage, is it a penalty after advantage?
"You can't let him shoot and then pull him back. It's either advantage or a penalty - it can't be both. The referee has gone against us on both of them.
"Overall, I thought we started well. Obviously the first goal is a mistake. We started the second half well again but major decisions have gone against us."