Two years ago, the club won the League Cup and then clawed back a nine-point deficit to Liverpool over the last five games to become league champions.
Now Kompany and his team-mates, also heading for the Champions League quarter-finals after a 3-1 last-16 first-leg win at Dynamo Kiev, want to do it all again.
Having edged out Liverpool in Sunday’s League Cup final after a penalty shoot-out, Manuel Pellegrini’s men face the Reds again at Anfield tomorrow in the league, desperately needing victory to reduce Leicester’s nine-point lead at the top.
“We don’t take anything for granted,” said Kompany. “We are stronger at the end of the season because we have the right mindset.
“I just think we need to keep showing people around that we can achieve a very good level of football.
“We showed it against Liverpool, we showed it in Kiev. It needs to carry on. We can’t make any mistakes anymore in the Premier League. That is what makes it an exciting competition.”
But Kompany knows how much confidence they will have gained from bagging the first trophy of the season, ensuring boss Pellegrini will leave with success before he is replaced by Pep Guardiola in the summer.
“Especially the fashion that we won it in against the club we won it against,” he added.
“It is a massive win. “Many thought we weren’t favourites just because we got battered by them at the Etihad in the league, but the team has shown signs in Kiev, shown signs against Liverpool of how we need to approach the rest of the season.
“Wednesday is a weird game because we are playing against a team that is going to be just as tired as we are.”
Full-back Pablo Zabaleta also recalled how City were eight points behind with six games left when they dramatically pipped Manchester United to the title in 2012.
And he added: “There are still 36 points to play for in the Premier League, which is a lot of games.
“We were in this situation before a few years ago even when we won the league that we were about eight points behind the leaders – and we still have a game in hand. We are Manchester City, we have talent and big players to try to recover those points that we lost.”