Glasgow's two wins in their four outings have come against Edinburgh and the Borders, with the latter two propping up the Celtic League after failing to secure a victory in their opening three matches.
But speaking after putting his squad through their paces at Murrayfield, Williams said: "It's very important that the pro teams win, but there's plenty of time to go. I'm particularly happy with what's happening here. We've had very, very good sessions.
"Generally the standard here has been markedly up again on our summer tour of Australia, which is what we were after, and I'm seeing progress.
"I think Glasgow are playing very well. I was very disappointed for them on Friday night because they played well until the last ten minutes, and I understand the Borders played well in Leinster, but were just cleared out in the last 20 minutes."