Pato admitted to Italian media that his relationship with Allegri was not the best which is sure to fuel more speculation that the striker could leave in the January transfer window.
French Ligue 1 side Paris Saint Germain are reportedly considering a €50million deal for Pato.
"I would like to have a more direct relationship with Allegri," Pato told the Corriere dello Sport.
"I won't say much more. If he thinks it is right to criticise me, then I have to keep my head down and work. I have to respect what the coach says.
"The fact remains, however, that if he has noticed something wrong with my game then he would be better to come directly to me so we can discuss it together."
In what could be seen as another swipe at Allegri, Pato felt it necessary to praise the coaching methods of his former AC Milan coach Carlo Ancelotti - who coincidentally is also being strongly linked with PSG as well.
"Carlo always spoke to me, told me what to do on the field," he said.
"If I have to improve [now] then [Allegri] has to recommend how. Champions must always move forward, they are expected to be the best.
"Every now and then Allegri will explain something to me, but a coach should always suggest to his players how to correct defects."
Should Pato leave for PSG, it could then pave the way for Carlos Tevez to complete his move to Milan.
Milan have indicated that they are keen to take the Argentinian striker on loan to the San Siro in January, but Manchester City are adamant that their former skipper will only leave the club on a permanent basis.