"After the disappointments of the last 10 days or so, this match was always going to be a difficult one," said Smith.
"Credit to Queens, they came back at us. It was a good final and Gordon Chisholm can be very proud of his team."
Nothing would make up for missing out on the Uefa Cup and the SPL, but he was thrilled to end the season with a cup double, having already won the CIS Cup.
But he said: "It has been an extremely tough spell for everyone involved and we can be a little bit happier than we were a few days ago.
"We are delighted to have the two cups this season.
"It's at least something tangible at the end of what has been an extremely good season for everyone.
Rangers were playing their 68th game of the season, including defeat 10 days previously in the Uefa Cup final.
Kris Boyd scored twice at Hampden and DaMarcus Beasley also found the net as Rangers fended off a determined comeback from Queens in the second half.
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And Rangers assistant manager Ally McCoist appreciated Boyd's lethal finishing, which made the difference between the teams.
"That's what he does best," the former Rangers striker said.
"Put the ball in front of him in the box and he'll score goals."
McCoist hailed the effort by First Division side Queen of the South, Gordon Chisholm's outfit having beaten Aberdeen 4-3 in the semi-finals to reach their first Scottish Cup final.
"They've been a credit to the First Division and to Gordon Chisholm," said McCoist.
"They've had a great season and it was a remarkable achievement getting to the cup final.
"They did Dumfries proud today."
