An unbeaten four-match run, coupled with Nottingham Forest's four-point deduction, has given Burnley fresh hope in their bid to avoid relegation and they have the chance to drag Everton further into the mire in a crunch clash on Saturday.
Burnley, who Kompany guided to promotion last season, remain in 19th place, six points behind 17th-placed Nottingham Forest and seven behind Everton with seven games remaining.
"I don't think about (the consequences of relegation), not when there are seven games remaining and everything to play for," Kompany told reporters on Thursday.
"The only thing I always try to convey as a message is that any scenario is one that the club has known in the past and never panicked in those moments so why all of a sudden should we? Should we portray a crisis?
"We know the urgency of the situation. The club has been there before, staying up and going down and the club has always done the right thing in the past."
Everton, who could yet face more points deductions having already been docked six points this season for breaches of Premier League rules, are on a 13-game winless run under former Burnley manager Sean Dyche.
But Kompany says he is only concerned about his own team.
"I have not delved too much into the fact they are on a winless streak. It's not really relevant to me. It is the game itself that matters," Kompany said.
The Belgian was also asked about his comments that Premier League referring was not good enough after being given an FA misconduct charge following his red card during Saturday's 2-2 draw at Chelsea.
"My comments on the standard of refereeing was just an objective and fair assessment," Kompany said. "But there is a lot of things we should have done better this season as well.
"I think there are ways to make it constructive, which is definitely not the way I did it on Saturday, but it is the way I am trying to do it now.
"But I have to move on. My main thing now is the game."
