The young Gers were forced to come from behind after the Danish outfit struck from the penalty spot inside five minutes.
Calum Adamson provided the leveller for the Light Blues with a spot-kick of his own nine minutes from time in a contest in which Rangers could count themselves the superior side.
Speaking to RangersTV after the draw, Smith commented: “I thought it was a good game.
“They scored a penalty quite early and we had a period where we were quite nervy for the first ten minutes.
“We got to grips with the game after that, and I thought from there we were excellent in both sides of the game. There’s some real positives in the 90 minutes.
“It was a different challenge against players that they didn’t know with different attributes.
“They then have to go and dominant something which is completely different to you.
“I thought every individual, whether it was physical, tactical or technical, stood up to that challenge.”
The Danish side flew out the traps in the first half and had opportunities to double their advantage after their early spot-kick.
However, Rangers wrestled control of the game and ought to have restored parity – if not completed the turnaround – before the half-time interval.
The momentum continued in their direction in the second half, and it was no more than they merited when Adamson squeezed his penalty underneath the goalkeeper in the final ten minutes.
Smith added: “[FC Copenhagen] were a real threat because they got their goal and you’re a bit worried that it could become two or three-nil.
“We showed a lot of character and resilience which you need against good teams, but we also showed quality when we found our rhythm and control.
“It was two different styles: they were a real threat when we turned the ball over, but when we were in possession we showed our quality and played our combinations.
“I thought a draw was a fair result in the end.
“You never know what the opposition are going to bring.
“I think when you look at the balance of both teams we played similar ages and it was a really competitive game. It was two different styles which made for an entertaining game.”