Killie suffered a rude awakening in their season opener when they were thrashed 4-0 at home by Paul Hartley's team.
Another 4-0 loss at Rugby Park soon followed, against Ross County, but Killie begin their second round of fixtures at Dens Park on the back of a run of one defeat in five Ladbrokes Premiership games.
And Smith, one of many summer signings, feels they are getting their rewards for hours of effort in training.
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"We saw on the first game of the season the performance levels Dundee are capable of," the former Rangers player said.
"If we don't match up and don't work hard and put in a good performance then we could get turned over again.
"I think every game we go out in we have to work hard after the way we started.
"Recently we have done that and that's credit to everyone; the manager, the coaching staff and players, because the last few weeks we've worked really hard and we are starting to get the benefits.
"Over the international breaks, when the majority of teams have days off, we have been in doing double sessions, with every aspect of the shape and fitness levels. It just shows you, when you put the work in, you start to get the rewards.
"It was always going to be difficult with the amount of changes that happened over the summer. I didn't think we would have started as badly as we did but that's football sometimes.
"We have come through that tough time and we're all working hard and Saturday is going be no different."
Smith has been moved into midfield in recent weeks following the acquisition of fellow left-back Kevin McHattie.
"I have played wide before which I didn't really enjoy but I really enjoyed it last week," the 30-year-old said.
"Over the past few weeks in training and in a few bounce games I have played there - we've done a bit of shape and I've been in there and I enjoyed it."
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