Warriors backed up last weekend's 24-12 win at Hampden with a 21-3 victory to keep the 1872 Cup at Scotstoun for a fourth successive season.
Speaking to the media after the game, Smith said: "To be honest, it was not our easiest night out there, let's put it that way. I thought Edinburgh stepped up again: they're at home, they're a proud team, which I think Scotland must be proud of as well. They've got a lot of heart, but in the end, I'm really, really proud that we stuck to the plan and got it done."
With the clock in red, Glasgow pressed in search of a fourth try that would have delivered a bonus point. Referee Hollie Davidson brought proceedings to a close after Dan Lancaster kicked the ball into touch with Warriors thinking a penalty advantage was being played.
"I thought there was a penalty advantage so you can understand why Dan kicked the ball there," said Smith. "I think we probably didn't deserve it, to be honest, but the opportunity was there and I'm a little bit disappointed not to get it."
Asked if he had spoken to Davidson about the incident, Smith added: "Not really. I didn't go and ask, but I think just before there was a knock-on advantage and that became a penalty advantage so maybe she confused the two. But I can't speak on behalf of her."
Taking nine points from a possible ten across the two 1872 Cup fixtures represents a strong outcome for Glasgow, who now sit comfortably inside the URC top four as the regular season nears its midpoint.
"I think we came with a plan a little bit different to last year's," said the coach. "It's a difficult period in this part of the season because emotion plays a big role. With Christmas and everybody seeing family, sometimes you get drained from emotion.
"We planned to bring energy in another way through fresh guys coming off and having played for a bit, with the idea that we can always have the other players coming in to finish the game regardless of what the score was."