To listen to member's worries about job is one of the work of manager?

Yesterday I went to dinner with my team members. One of them is the freshman and he was scoled. I looked him down. So I invate the members include him the dinner.

He said "I worried about the reputation of my team. I know I didn't do good job, so nowadays I couldn't work freely, always I scared about my work". I think on this sitation, I shouldn't advice, rather than I should listen to one's talking. So about 30min I keep listening. Actually it's harder than to talking. But it's the work as a manager I think because manager's misson is encouraging team and make the higher quality output. 

After the dinner he looked better, so I was satisfied the time. On my way home I wondered that it is really manager's work. On one side, it's of cource manager's work because one of the your mission is to manage the team. On the other side, it's not your work because one's mind of work should control by ourselves. We work for client, so if we can't work and control our mind, we shouldn't work on same team.

After all I think about it now, I should managing team is my misson because we work with team, and output for the client is our team output. So I should encourage and support my team members. I think I won't change this position.