Kennett said on the Hawthorn website on Monday, "we are about making history for the club this year, not just next or the year after."
But Clarkson would not commit to a time frame for winning the club's next flag.
"We want to progress as quickly as we possibly can," he said.
"We've put ourselves in a position that we can go deep into finals, and who knows, as we've seen in years gone by with Essendon winning in '93 and Adelaide in the latter half of that decade, if you get momentum in finals anything can happen.
"We set very high standards at the club and the demands are great, but that's the robust environment of this competition.
"We want to go as high as we possibly can and hopefully that's a flag, but we also are realistic to know that it's a really tough gig winning AFL premierships."
The Hawks face Collingwood this Friday night in another blockbuster clash at the MCG, and Clarkson said his side would need to improve its ball use if it wanted to end a run of two consecutive defeats.
But he believed the team had learned from the experience of last round's much-hyped clash against Geelong.
"We need to be a little bit more polished with our use of the footy in crunch times of the game," Clarkson said.
"I think it was an enormous experience for our whole club. For our players to play against quality opposition in a finals' like atmosphere on Friday night was first class and I think we'll only be able to measure the true value of it in time."
Clarkson said that for the younger players in the side, who had not experienced a finals-like atmosphere before, one of the biggest challenges was the noise level.
"You've got to yell so much louder to win the ball (because) using your voice to attract attention to yourself isn't anywhere near as great on a night like that."
