Moyes has always been a good manager who stumbled across 3 consecutive crap positions where he always going to fail. I think Moyes is professional enough to filter out the white noise from the fans and get on with his job at West Ham to be honest.
You've got to have thick skin to be a good manager as ultimately they all receive criticism at some point in their career. Whether it's results, transfers, style of football, interview style etc, there'll alway be something that some fans don't like.
To spin it back around onto Boro a bit, Carrick is really experiencing his first test of this and it is a big test of his resolve. At the moment he's still got the backing of the fans, what was the poll on here, 80% stay, 20% sack? But there's still a lot of that 80% who starting to feel a bit disgruntled and becoming more critical of Carrick and some of his selections, the way he answers questions, the way we pass out from the back etc. If Carrick is going to go on to become a top manager, he needs to come through this and turn it round.