Ole Gunnar Solskjær’s men trail 1-0 from the opening leg of their quarter final.
German international ter Stegen admits United will be like a wounded animal.
He knows the English giants remain capable of producing a famous fightback like the one at Paris Saint Germain in the previous round.
“We want to go out and master the game”
Marc-Andre ter Stegen
So he has urged Barca to be ruthless and finish off the job in hand.
The goalkeeper said: “We are facing a team who is eager.
“They have had some games away which they won, and of course the advantage is not so big for us.
“We want to defend it and uphold it – but we want to state our superiority and for that we need to play a good game.
“They are very quick. You always have to have be alert.
“I think it’s the key to winning this very difficult game. They know how to play in a very calm way. They made things really hard for us in the first tie.
“So we want to go out and master the game, have the ball as much as possible.”
Ter Stegen wants no repeat of Barca’s shock collapse to Roma at this stage of the competition last season.
Barca won the home leg 4-1 but lost the return game in the Italian capital 3-0 to crash out on away goals.
Ter Stegen added: “There is not much to be said about what happened in the past.
“It was hard of course but it’s another year on and we got over it.
“We don’t want that to happen again. We need to bear it in mind and look forward and this is a good time to achieve a good success for us, with all our fans around us, so hopefully we will beat them.”