Next up is another Heineken Cup encounter with more familiar foe as the Warriors travel to Newport to face the Dragons at Rodney Parade.
It's a tie that won't affect who qualifies for the knockout stages but Kellock is keen for his side to use the match as a springboard to Magners League success.
"It has to be a marker," said Kellock ahead of Sunday's trip to South Wales.
"Us and the Dragons know each other well and it's another funny dynamic with neither team pushing for anything. That'll make it really important that the guys step up during the week, that the leaders lead and the right attitude is taken into that game.
"We need to go down there and play well so that we can become more consistent. We need to kick start our Magners League season at some point and, over the last few weeks, I think we've been beginning to do that."
The atmosphere in the Glasgow camp is understandably a good one following such a major victory, especially as Wasps had it all to play for whereas the Warriors were competing for pride alone.
But Kellock insists that the positive mood throughout the squad hasn't just been brought about by last weekend's triumph. The man who led Glasgow to an unexpected Play-Off spot last term is adamant that his squad have always been a united bunch, even when results haven't gone their way.
"We're as tight as we've ever been as a squad and you win games from that," added Kellock, whose side currently sit 10th in the Magners League standings but haven't given up hope of a top-four finish.
"We're working so hard. We're realistic and we know where we are. We really came together in that Toulouse game in the Heineken Cup where we went over there in difficult circumstances.
"Although they beat us convincingly in the end, at 60 minutes we were right in the game. We left everything out on that park.
"We've set that standard that, whenever we play, it's about 100 per cent commitment. If it's good enough, then we'll win. If it's not, then we have to say 'well done' to the other team.
"We've shown already what we can do. We've got to push on, get the right results and move further up the table. We're not happy with where we are at the moment and the only thing that's going to stop us feeling that way is a few better results.
"With the position we've put ourselves in, it's a cliché but we have to take every game as it comes. We need to edge our way up there and then we can start setting longer term goals.
"I like the way the league splits itself up so that when we come into the next set of games after the Heineken Cup, it's about trying to edge up and edge up. It's not a million miles away from us but it's a difficult task."
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