Managers must prioritise. You have to keep your eye on the prize, potentially at the expense of everything else.
In this case, he prioritised Hart and the first eleven over Given. He made a public display of confidence in Hart, and this extended to the rest of the defenders and midfielders. After throwing away points through two silly mistakes, he gave them the opportunity to put things right. They kept two convincing clean sheets, and confidence is fully restored. Against that, Given's unhappiness is small beer.
This is an example of the needs of the many outweighing the needs of the few, the first team coming before a fringe player. It's worked. Mancini's man-management has demonstrably worked.
It's up to Given how he interprets what happened. Going to the press, before you have exhausted all avenues of internal communication, is selfish and short-sighted. Unhelpful to the club, the manager, and your team mates. Forgiveable, as his frustration is natural... but it won't be forgotten.
It's not acceptable behaviour, and anyone who ignores that, and focuses on whatever they imagine Mancini may or may not have done, has simply lost perspective.