The defender withdrew from the England Under-21 squad ahead of Tuesday night’s friendly against Sweden and manager Pearce disclosed to the media that the 20-year-old was suffering from shingles.
However, Sir Alex is disappointed with Pearce for revealing Jones’ condition, suggesting that the Football Association should have instead treated the matter confidentially.
"What about doctor confidentiality?" Sir Alex told reporters.
"That was a conversation between our doctor and theirs and shouldn't have gone any further. It is something we have to address."
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Sir Alex has already been fined £12,000 this season for controversial comments the 71-year-old made about assistant referee Simon Beck, although the FA has said it will not be responding to his accusation on this occasion.
Jones has since overcome the problem and has been declared fit for Sunday's Premier League clash with Everton at Old Trafford.