The Dark Blues ran out convincing winners over the Irn-Bru First Division leaders as they powered into the quarter-finals, where they will face city rivals Dundee United
"It's a very good win all things considered," said Smith, whose side are 14 points adrift at the foot of the SPL. "It should give the players a lot of confidence for the rest of the season."
He added: "The goals all came from different players and there was a lot of decent football on show so it's all positive.
"We will hopefully take encouragement from this and there's no reason why we can't.
"This was always going to be a dangerous tie against a good side but we handled it well and I'm very happy with that side of things."
Second-half goals after the break from Lewis Toshney, Colin Nish, John Baird and Declan Gallagher saw Dundee go through to the last eight after Michael Tidser had cancelled out Jim McAlister's opener to see the sides go in level at half-time.
Morton boss Allan Moore was quick to admit his side were never at the races.
He said: "It's so disappointing from our point of view. When you look at the goals we lost that was our own fault with nobody else to blame.
"It just wasn't good enough and we can't make any excuses. At the end of the day we didn't do the basics right, especially in defence."
- Sports & Recreation