His decision was a blow for the Scottish champions, who had headed into the interval a goal ahead thanks to a Steven Davis strike.
But Smith was far from surprised by the referee's decision, admitting: "I thought there was a possibility it would be called off when I watched from the stand in the first half.
"The water was starting to gather and I thought it would be a decision the referee would have to take.
"I don't think we can complain, although we are disappointed after working hard to get 1-0 up. I don't think I can argue with the referee's decision, I think he was quite right."
Asked whether the match should have been called off before the start, Smith replied: "It was just one of those circumstances that happened.
"He was right to abandon the game and he was also right to play the game because I don't think it would have been justified to put the game off at the start.
"In fact, I thought the referee handled the game well today despite the circumstances."
Some Rangers fans were clearly unhappy with the referee's decision and, although disappointed himself, Smith refused to lay any blame with Tumilty.
He said: "Everybody wants to play but we have to accept the decision and I stress again that it was the right decision.
"The referee didn't want to put the game off either so it's just one of those things that we have to accept."
Davis was unhappy with the decision to abandon the match after notching his first goal of the season, claiming he had played in worse conditions than those at Tannadice.
He said: "The match started at a good tempo and the decision could probably have been made before the game because we can feel a bit aggrieved after being 1-0 up at half-time.
"It was a bit disappointing it getting called off. I've played in worse, I know that much.
"Once you get to half-time and you are 1-0 up, you are always going to feel a bit disappointed. That was the case today.
"Obviously the conditions weren't good but you would hope the decision would be made before the game."
Tumilty stated player safety as the reason why he called a halt to the match and Davis conceded he could not really argue with the referee's call on that basis.
He said: "It's just disappointing. But we have to put it to the back of our minds now.
"We are aggrieved at the minute but once we get our heads around it we just have to get back to winning ways in our next game.
"People have to make these decisions and the last thing you want is people getting injured because of the conditions so maybe in that respect it was the right decision."
United boss Craig Levein sided with Tumilty, saying: "I felt the referee didn't really have an awful lot of choice to be honest.
"If the rain had stopped at half-time and there was a chance of the water being soaked into pitch, I would have questioned whether it was playable or not. But the rain was just incessant and there was no way that was going off."
Despite trailing at the break, Levein claims he and his players were disappointed to be denied the opportunity to haul themselves back into contention.
He added: "It's not often that the manager of the team who is behind when a game gets abandoned is disappointed but, although we were behind, I was thrilled with the way we were playing.
"When I told the players the game was off they were devastated because they knew themselves they were on form today and felt they could get back into the game and that they could win it.
"They were absolutely gutted when I told them the decision and that is really encouraging for me. They should take a lot of confidence from that."