A tug in the box on John Baird after 35 minutes by Killie full-back Ross Barbour irritated Smith. Referee John Beaton ruled it was an accidental clash, but the Dens boss argued differently.
Smith said: "I think it is a definite penalty. Baird's been held back in the area. Anywhere else on the park, it's a foul. So why in the box?"
He added: "I thought we did enough to win. We hit the post, had another cleared off the line. We're happy with the performance but just couldn't put the ball in the back of the net.
"I'm delighted for the defence, as they have a hard time but have managed to get a clean sheet. Now it's about building on that and sticking the ball away."
Kilmarnock assistant boss Jimmy Nicholl took over dug-out duties while manager Kenny Shiels sat out the first of his four-game ban for comments made about fourth official Andrew Dallas but while he was not there on the sidelines, Nicholl insists the players must continue to play to the standard set by the boss.
He said: "It wasn't bad but it wasn't great either. But then a clean sheet and a point away from home is something to build on.
"The manager's standards are so high when it comes to passing. He wants us to get the Spanish lad Borja Perez on the ball for us to create things for Paul Heffernan. He wants that happening all the time but it can be a fine line. It doesn't happen all the time.
"They have always got to try and reach those standards. We're not asking them to do anything they can't do. They are capable of producing this standard of football.
"But the opposition are out there trying to stop you from doing it, so you have to give them credit as well."