Speaking to Premier Sports, Smith said: "We believe we can do well in the competition. We have fallen short quite a bit over the years. We would like to progress on that, but I'm not going to add any extra pressure on us.
"We need progression and we need to handle the last 25 minutes of a game better and not start with a deficit like we've had for the last two weeks, so I'd rather concentrate on that.
"Getting through the pool is the first objective, then we will see after that. Ending top of the pool will win nothing - it is the progression beyond it that's going to be important. This was important to get belief. Against a world-class club team like Toulouse, to get one over them was the most important thing.
"The players here are very competitive and they want to make the next step. They have been on the losing side in important games for a long time, so you have to have a heart for these boys."
Glasgow's attention now turns to the first of the URC double-header against Scottish rivals Edinburgh, with the first leg at Hampden Park next Saturday before the return fixture at Murrayfield on 27 December.
"This [win over Toulouse] also creates a lot of expectation," he added. "It is not even Christmas yet and there is a lot of rugby to be played. We have only played three games in a 10-week block. There is an international window coming up with the Six Nations, so these players are going to be challenged. To manage them through this next block is more important than the results, to make sure we continue to progress and grow.
"It is easy to build a team up to say 80%, but that last 20% takes time. We need to improve still on that. We are not going to get ahead of ourselves. We have won nothing yet. We just know now that we can do that. That is the message this week."