United are looking to bounce back from their worst season in 50 years and the defender is convinced that substantial improvement will be made during Amorim's first full campaign in charge at Old Trafford.
Speaking during the club's pre-season tour in the US, Shaw said: "I think his mentality, his demands [show he's the right man].
"He's extremely tough on the group. He leaves no stone unturned and I think there are no stragglers in this group anymore. I think everyone has to put the team first. He's made that very clear.
"I think he's picking players on how he feels will be best for the team and that's his choice. As players, we're fully behind him and fully behind on his ideas and what he wants to implement in this team. We feel like a real team, especially this pre-season.
"Since I've been back, the group is so together and I think that's something that we need to keep to make us more of a family and everyone all together and we're all driving in the same direction."
Shaw believes that the team spirit at United allows them to aim to win the Premier League title, even though they could only finish 15th last time out.
The full-back said: "I can't be any worse than it was last season.
"I was so low last season, so I think anything but that. I feel good and I think especially this pre-season.
"Obviously, I didn't have a pre-season last season either, so I think it's really benefiting me to be able to just be fit and train with the team and get minutes.
"I'm enjoying that. Aims wise, I think the aim has to be winning the Premier League.
"I know people will be questioning me for saying that after last season, but it has to be that. It's not just me who thinks that. I'm sure the whole team, if you ask them, they all have the same aims.
"Even the manager, I'm sure he probably wouldn't say it in the press, but we all have to have the same beliefs and ambitions. Like I said, that real family feeling together, and we all strive for the same thing."