The 32-25 victory over Edinburgh at Murrayfield was Glasgow's fifth win in consecutive matches in all competitions.
Smith says he would not waste any time counting the victories, but he believes his squad are seeing the benefits of their hard work in pre-season.
Speaking to Viaplay after the match, Smith said: "We didn't count the wins. It is about getting better every week, but we appreciate having the scoreboard in our favour.
"I'm glad for the club. All credit to the players and coaching group, they have been exceptional in this period.
"There were some decisions made in pre-season on how we want to approach the campaign and they have bought into the philosophy. We think there is a lot to work on but if you have this buzz in the changing room it will help.
"The first half showed that expectation is our enemy. There was a lot of expectation around us and I felt that drained our energy, so the quicker we get rid of the expectation around our next performance the better it will be.
"I'm really delighted for the boys. They made some sacrifices over the Christmas period. We had a plan and they stuck to it, and I thought the second half, the energy the boys brought from the side and the way they reacted from the half-time talk, was fantastic. We lacked a little of belief and one or two things said at half-time helped us align again."
Sione Tuipulotu took the man of the match after a fine all-round display. The Scotland centre's leadership qualities have also come to the fore this season. "I'm glad for Sione - he really stepped up," said Smith.
"It was a tough pre-season, as it was for most of the guys, but he kept on going and the continuity he has got with playing a couple of games helped with his performance tonight."
Next up for Glasgow is a URC match against the Stormers, the current champions, on Sunday 8 January at Scotstoun.
"We've got the Stormers coming - they are the champions of this competition - and it is going to be a tough afternoon if we don't find our feet immediately," Smith accepted. "With them being the favourites, it will be good."