The reigning champions took the lead in their opening fixture with Southampton, but then allowed the newly-promoted side to score twice at the Etihad Stadium, risking an embarrassing start to the campaign.
Roberto Mancini's men did manage to bag two goals in the last 20 minutes to defeat the Saints, but they again found themselves trailing when they travelled to Liverpool on Sunday.
Carlos Tevez was gifted a late equaliser when Martin Skrtel got a back-pass horribly wrong, but the Dutch midfielder insisted that chasing games is not something they should be doing, suggesting this season will be harder than last as they are now the team to beat.
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The 27-year-old told City TV: "I don't know what it is. It is a bad habit.
"We picked that up from the last game of the season against QPR and have continued that in these first two games of the new season.
"We have to improve and show that we are up for the test wherever we go, away or at home.
"We have a lot of qualities in the squad but we just have to improve.
"It is not going to be an easy season. Wherever you go everyone wants to beat the champions. We have to stand tall with each other and improve."
City were outplayed by the Reds for large periods of the game at Anfield, and were fortunate that Skrtel's error handed them a point.
The Holland international insisted that a draw was a good result after they fell behind twice, acknowledging that an away clash with Liverpool is never an easy affair.
"We played some decent football at times, not all the game but at least we tried a lot of times," he continued.
"It was a pity we let the goals in but on the other hand we showed the determination to come back twice and get away with a point.
"It is not always easy to play football at Anfield. We knew that from the last couple of times."
Tevez scored his 100th goal in English football at Anfield, and his third of the season after netting against Saints in the league and Chelsea in the Community Shield.
De Jong praised the Argentine for his sharpness at the start of this season, after a number of well-documented bust-ups last term, stating he expects the striker to be lethal this campaign.
"He looks quite slim," the midfielder added. "He always had a little belly but that is gone now at the moment! All credit to him.
"Don't get me wrong, it is always hard to get him off the ball, but I'd rather have a slim Tevez than one with a belly.
"As long as he scores goals for me it is okay. He is on fire at the moment and a Tevez on fire is good for any team wherever he is.
"I am just glad he is still part of this City team and if he continues like this he will score a lot of goals this season."