Dani Ceballos slotted home a low, angled drive in the 91st minute to win the tie in dramatic fashion, after David McGoldrick's hooked finish just a few minutes earlier looked to have ensured extra time at Bramall Lane.
Mustafi said, "Normally I think before we conceded there is the moment we have to kill the game. But we didn't and conceded. But it shows character. It helps the team to get back confidence. Today we didn't give up, even when they equalised. You have to prepare for extra-time but got rewarded.
"Sometimes you have to see what the opponent does. There were a lot of long balls. It is not always easy to find solutions. This team believes in how we want to play football and tries things even when it doesn't look as good as it should. We have to believe in the process."
On team-mate David Luiz, who has struggled with form recently, Mustafi added: "At the end of the day we are human beings and make mistakes. As a defender life is not always easy but he is experienced enough and is a fantastic team-mate. For me he is a big personality and I am happy to have him on the team."