A Lee McCulloch double secured the win, after Andrius Velicka had levelled for the Tynecastle side, allowing Rangers to close the gap on leaders Celtic to just two points in the Clydesdale Bank Premier League.
The performance may not have been vintage but Smith insisted: "The win was more important. It was always going to be a difficult match for us, I don't think there was any doubt about that.
"We got a little bit of good fortune at the end to win the game which was the most important thing from our own point of view after our efforts in midweek.
"We've had that experience throughout the season - playing Champions League games and then having to play league games on the Saturday as well.
"The added disappointment is sometimes harder to overcome but I didn't think that was a major factor today. Today's game was one we were just pleased to get over with with a win."