A win at Tannadice would have allowed Rangers to extend their lead at the summit to a nine points but the SPL leaders were grateful for a draw following a thrilling six-goal contest.
He said: "Everyone was quick to say that last week's (Old Firm) game was a league decider and I was quick to point out that we do have to play other teams.
"In Scotland, I don't think we give enough credit to the amount of effort that teams put into their games.
"That has happened and it was always going to be a really awkward game for us here."
And, with Motherwell, Hibernian and Dundee United all still vying for third place and a UEFA Cup spot, Smith believes there could be more difficult weekends ahead for both halves of the Old Firm.
He added: "For the last few seasons the third-place team has been in position for a period, as have Celtic in terms of being champions.
"This season, you have two teams fighting for the championship and three teams fighting for a European place. The last period of the season will always be a difficult one."