Cole feels Chelsea should have more Premierships
However the 28-year-old insists the team have learned their lesson and are determined to win their first league crown for four years.
"If you look at the two titles we won at Chelsea, it was too early for the club," he told the News of the World.
"Everybody took their foot off the gas while Manchester United got better. We won't make the same mistake again.
"We still won trophies, got to the Champions League final and finished second in the league twice, but it has to be first or nothing for a club like Chelsea.
"If you're not winning you are not happy. I don't care who else wins it, I don't begrudge anyone else success and United are a fantastic club - but we need to be winning the league four times out of five.
"With the money we have spent, the players in our squad, the ambition we have and the support we enjoy, it has to be the aim."