Harsh stakeholder criticism

Did the team meet the Sprint Goal?

Also bear in mind that the Product Owner is under no obligation to invite a stakeholder to a demo, or even to a Sprint Review. It's a privilege that's being extended, and if a stakeholder can't provide helpful feedback they may not be invited again.

It in the scenario above, it's a case of dissatisfaction either caused by over whelming expectation or demands. A team can only accomplish as mush as their capacity and skills permit. On another hand, this could be an opportunity to exploit to understand how the PO and Stakeholder communicate. 

Criticism is negative on the team's moral and the stakeholder needs some coaching on how to interact and collaborate with the team and on how to give his feedbacks.

As you said, communication is key!

It's clear that talking to stakeholders about their approach is essential.

But why does the person providing feedback behave in this way?

Disappointed expectations are not usually the only reason. Did the stakeholder feel that their criticism had not been taken seriously until now? Were the sprint goals communicated clearly, and was it made clear why it was not possible to do more?

Always consider that the stakeholder may be right.

In my professional experience, I have never met anyone who was stupid. The stakeholder's belief that their expectations are reasonable is based on their experience and knowledge. My belief that they are excessive is also based on my experience and knowledge. While I may have more experience, my opinion is probably, but not definitely, correct. Discussing these differing views and the reasons behind them can only help both sides to learn and adapt.

Another approach would be to talk to the team.

Yes, criticism presented incorrectly can demotivate a team. 
However, feedback is always a gift, even if the person providing it is not trained to deliver it 'correctly'.
Train the team to separate the content of the criticism from their emotions and think about it. Take the criticism seriously, but don't necessarily act on it.
 

... the stakeholder needs some coaching on how to interact and collaborate with the team and on how to give his feedbacks

I think you gave the answer. Stakeholders are usually not experts in Scrum or team dynamics. Many come from traditional project environments where direct criticism of delivery teams was more common, and they may believe they are helping by “setting the team right.”

Part of the Scrum Master’s role is to coach stakeholders on how to collaborate with the team and provide constructive feedback.

At the same time, the team should not take such criticism too personally. Stakeholders bring business expertise, but they are also just people with their own communication styles and limitations. Some resilience from the team will help.