But Jefferies stressed Kilmarnock's main aim is always to ensure they remain among the elite band of clubs, and claims they have exceeded realistic targets in previous seasons.
He said: "For us to make top five and a cup final, we overachieved with what we were working with and what we had to do.
"You cannot guarantee that every year, and someone always gets a turn.
Jefferies has seen Hearts drop into the bottom six of the Clydesdale Bank Premier League, and insists his former club's situation is entirely different to how Kilmarnock should be judged.
While Hearts have a high wage bill and large squad, Killie have had to scrape together a team at times due to a lack of depth.
"It's been a bad season for Hearts, but they have the resources to be in there and we haven't, unless someone comes in and ploughs money into the club," said Jefferies.
"The remit is making sure Killie are in the SPL full stop. The top six drives players and management."