It's not because of what media says. Allegri has been overly defensive in his statements since the beginning of the season. The fact he was having a little attack with Marotta and Paratici shows a lot of stress, regardless of what was said. And it is comprehensible, because the $#@!ty performances are indeed exhausting and causing a lot of criticism.
He's spent 6 months saying "what matters is how the team will play in March". The guy is clearly getting worn out, and only great results in Europe can change that imo. Nothing to do with media.