Although they are just one point off top spot in the Barclays Premier League, City have been particularly disappointing in the Champions League and face a fight to qualify for the knockout stages after picking up just one point from three group games.
That has led to some cutting analysis from outside the club, and Kompany, outstanding at the heart of City's defence in the last campaign, has also found his form the subject of scrutiny.
But the Belgian said: "Personally, I don't ever get affected by it.
"I just keep living the life and keep working really hard. If one day goes a little bit less than another, I know I have at least done my best.
"By being patient and keeping doing what you have done to get success in the first place, you'll get there again. It is a very difficult thing.
"People around the club get wild and excited but I stay very calm.
"We'll be here in a couple of weeks or months and maybe everyone will be praises and smiles. It is going to happen. Everything takes time."
Criticism of City intensified after the midweek loss to Ajax in Amsterdam left them needing a "miracle", in the opinion of manager Roberto Mancini, to reach the next stage of Europe's elite club competition.
Mancini came under fire for changing his formation too often during the game and defender Micah Richards said he was not comfortable with the change of system at the back.
Some reports claimed the City squad was heading for mutiny because the players do not like the changes Mancini has made this season, but Kompany, who helped the team beat Swansea 1-0 on Saturday, dismissed that as nonsense.
The 26-year-old said: "That's funny. I don't like to get involved in this but sometimes I do.
"I never have a problem with performances being down or up. People have the right to have opinions on performances, but the stories are based on things I cannot even relate to, and I am in this team.
"I started my career to play football and be the best footballer. I expect journalists to tell the truth and do the job for that.
"That is just sensationalism, nothing more."