The Black Cats are currently bottom of the table and five points adrift of safety following Wednesday's thrilling 4-3 defeat to Chelsea.
However, Borini, who is on loan at Sunderland from Liverpool, believes they can take great encouragement from their display against title-chasing Chelsea in their battle to avoid relegation.
"We don't feel like the worst team in the Premier League, because we are not the worst," Borini told the Northern Echo. "That is the mentality that we have to keep. We have to keep a winning mentality and know what we are capable of.
"If we play the way that we did against Chelsea, we won't get relegated. We do not deserve to be at the bottom. Playing like that against a top team was good, but the key will be doing it against our rivals at the bottom.
"The manager told us that even Jose Mourinho congratulated us on our performance. Mourinho said that he was surprised by the performance, and that is good."
Borini believes Sunderland have progressed under new manager Gus Poyet despite their league position.
"We are a different team from when Poyet took over," added Borini. "We lost 4-0 that day to Swansea, but he has started to pick the right team and build up a way of playing that is different. And he is trying to pick the best players now.
"We are capable of playing good games and doing well. To score three goals against a team who won two European trophies in two years was a positive - but we obviously conceded four."