Glasgow lock Tim Swinson insists Dave Rennie is in good company after failing to be satisfied with their opening two Guinness PRO14 victories.
New head coach Rennie claimed his side could do better after their 31-10 bonus-point win over Ospreys on Saturday.
Swinson said: "I don't think it's just the coaching staff, as a playing squad that's what we have demanded from ourselves over the last few years. We are not happy with mediocrity.
"That can be down from (captain) Ryan (Wilson) through the leadership group, right through to the young academy guys who have been here for three months.
"Everyone wants to achieve and be better, we want to play a really good standard of rugby and we want to do that for 80 minutes.
"We have got two great results and nine points from two games is a good place to be, but if we focus on results rather than the process we will miss a few things. Our process hasn't been great so far but we have been improving week to week."
Swinson feels subtle changes following Gregor Townsend's reign have made a difference to their play under Rennie.
"He is very much into an up-tempo sort of game, which is quite similar to Gregor, but there are slightly different changes to our tactical awareness, which is interesting to take in," said the Scotland international, who is set to make his 100th Warriors appearance in Saturday's clash at Cardiff.
"You really see a different view on how to play rugby. Small changes have made an effect on our game."