The Black Cats have been pulled into a battle to beat the drop to the Championship in recent weeks, but a 1-1 draw with Stoke City lifted them three points clear of the bottom three with two games to go.
Despite the gap, Mignolet is adamant that the club do not need to worry about any of the teams around them.
"There's a lot of ifs and buts, but we just have to worry about ourselves. We know we've got it in our own hands. There's no team we have to worry about, all we have to do is worry about ourselves," Mignolet told the Northern Echo. "Now we need to get the rest we need, we had a hard game against Stoke so we need to recharge our batteries and go again on Sunday, we really don't need to look at what other teams do.
"We will try to block out what every other team is doing. Everywhere we go on the streets, everyone's talking about ifs and buts and what might happen.
"We have to be professional and deal with that and not let it affect us. We have to deal with our own performances and if everyone puts in a performance like we did in the second half against Stoke there will be nothing to worry about."
Sunderland host Southampton on Sunday.