Killie moved eight points clear of bottom side Dundee United with a 3-0 win over St Johnstone on Saturday.
With five games matches remaining, the target is to make ground on Hamilton who are four points better off.
"Rangers are coming up and, if Hibs manage it too, then the league gets it's wow factor back," said Clark.
"You want to be part of that and it gives me the chance to attract the kind of players I would like to make sure the club isn't in this situation again.
"The club has been dicing with survival for many seasons and that needs to change."
Clark, 43, arrived at Rugby Park in mid-February on a three-and-a-half-year contract.
The former Blackpool and Huddersfield boss went six games without a victory, with the team scoring just one goal, before a Kris Boyd double helped see off St Johnstone.
Kallum Higginbotham was also on target in a comprehensive victory.
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"We'd been creating chances, so it was never an issue," Clark told BBC Scotland. "It was just getting the players to have the confidence to take more risks and finish off those chances.
"In previous games I'd been pleased with our level of performance. There was only one indifferent performance against Ross County when we weren't at the required standard.
"I knew, with a little bit of luck in front of goal, that the results would come.
"We had Hearts, Aberdeen and Celtic in that run and we should have taken points in those games.
"We've got one (win) but we still need a few more."
With Clark arriving after the transfer window, his recruitment has been restricted but he has managed to bring in Julien Faubert, along with Miles Addison and Alex Henshall.
"I felt we lacked pace and power and that's what I've tried to address in the out of contract market," said the former Newcastle and Fulham midfielder.
"When I came through the door we had one of the worst defensive records in the league.
"You've got to start from the back and we've been stronger. We've had three clean sheets.
"We need to start scoring more and hopefully Saturday is the start."
Manager Lee Clark is urging Kilmarnock to build on the first win of his tenure and make sure they are part of an exciting top flight next season.