When Arsenal signaled the midfielder's substitution, the home fans present at the Emirates Stadium broke into cheers before the Swiss man was booed off the field in the second half during their 2-2 draw with Crystal Palace in the Premier League.
Carragher does not think Xhaka can continue with the armband but says previous captains such as Laurent Koscielny, Robin van Persie and Cesc Fabregas behaved much worse than the 27-year-old has.
The Arsenal squad initially selected the Switzerland global to be club captain in a ballot held last month.
The Arsenal role makes sense for him because he's familiar with the league and a lot of the players on the current squad, but it's hard to tell if the Gunners would have any interest in Mourinho.
'He trained normally with the group but he is devastated, ' said Emery on Tuesday. His behavior was flawless in training, with the group and club.
Carragher believes there should be sympathy for Xhaka even though he hasn't apologised.
"For instance, our dialog this morning was as a result of I wished to take heed to him about how he's pondering now to assist us and be with us tomorrow. Really, he knows he was wrong and he feels inside very deep".
"I don't need his apology. I want now like in the pre-season, like a month ago, for him to help us on the pitch". "We've got had this morning an excellent dialog, Mesut and Me, and I stated to him I haven't modified my thought about him".
'My ideal future is to watch again Xhaka playing and every supporter supporting him.
"I think it might be hard for him to continue as captain now because of what happened", the Liverpool legend said on Sky Sports.
Xhaka will not play on Wednesday night in the EFL Cup clash with Liverpool at Anfield, although a number of first team players were always going to be rested for that match.