The Warriors fought back from 12 points behind to lead 33-26, before Rory Darge and Sam Talakai were both shown yellow cards as Glasgow were reduced to 13 players for the closing stages.
Ulster eventually drew level through Juarno Augustus, although Glasgow still had an opportunity to claim victory when George Horne's late penalty struck the upright.
"I think it's a bit of both - but this is a start of the season match," said Smith when asked whether frustration or disappointment was the overriding emotion.
"There are a lot of reasons we're still a little bit rusty but I thought there was some good fight.
"It feels like a loss but it's definitely not a loss. We've got enough points out of this and enough lessons learned that will serve us very well in what needs to happen next."
Smith highlighted game management as one area in which his side can improve, while also accepting responsibility for asking his players to challenge Ulster from deeper positions during the contest.
"Game management is the first thing [we need to improve on]," he said.
"Part of that is down to me. I asked the boys to ask questions a little bit further out. So I'll take responsibility for that.
"We changed it in the second part of the game but also gave away some easy turnovers. But I think it's an easier fix than some people might think. Hard work and good understanding."
Despite being down to 13 players, Glasgow had the chance to win the match when Ulster were penalised at the breakdown with four minutes remaining.
Horne's effort rebounded from the upright, but Smith was quick to dismiss any suggestion that the scrum-half should shoulder responsibility for the result.
"I think that proves my point," said Smith of the decision to kick for goal.
"The thing is, there's times when that's necessary. George missed but I'll never blame a kicker having been one myself.
"You get it sometimes right and you get it sometimes wrong. He's made some incredible kicks this evening anyway to put us in that position.
"But Ulster shouldn't have had so many points. That is my feeling. It's not about what we could have scored, I think we could have prevented them from scoring more."
There were nevertheless plenty of positives for the Warriors, who scored five tries through Josh McKay, Jamie Dobie, Sam Talakai and a Kyle Rowe double to secure an attacking bonus point alongside the two points for the draw.
The result also leaves Smith's side unbeaten after the opening two rounds of the BKT United Rugby Championship, following their 26-20 victory over Munster at Thomond Park on the opening weekend.