DTH van der Merwe, Henry Pyrgos, Rob Harley and Finn Russell all grabbed tries in the triumph but Kellock insists the victory will have many long-term benefits.
And the 33-year-old, who leaves the Warriors after nine years' service to take up an ambassadorial role with Scottish Rugby, admits it's time to strike while the iron is hot.
"We have great people here and the advantage of playing rugby in a small country is that we can share it. If there is one thing that this trophy needs to do, it is to push the game further," Kellock told the Glasgow Evening Times.
"They all need to benefit from the fact we are a championship winning team. That will come from learning and from us getting out and promoting rugby.
"We need to get as many people to come in for a conversation with Gregor Townsend, the head coach, or with the strength and conditioning guys and tap into their knowledge.
"Any club that is connected with this place has to be better because of this. It has to trickle down, not just to clubs but to schools as well."
Follow us on Facebook, join the conversation on Twitter, sign up to our YouTube channel for extensive match highlights and sign up for our newsletter for regular updates on the GUINNESS PRO12
63x46.png){kind=logo}