Saturday afternoon proved to be a frustrating one for Sam Allardyce's side as, despite numerous chances for Jermain Defoe, Lee Cattermole and Borini, they failed to take three points off of Tony Pulis' side.
Never say never
However, the Italian forward, who was a major player in the 2013-14 'great escape', believes that it is way too early to write off the Black Cats just yet with a crucial trip to Carrow Road still to come.
Borini told the Chronicle that the club have been in "worse situations before" and so he is convinced that the team can stay up. The gap is only "four points" with "seven games to go," and Borini is adamant that "teams will still drop points".
He continued, saying that he is confident that the Wearsiders can "get wins" against the teams at the top because the top flight is "so crazy this year".
A double-header of matches at the Stadium of Light will end next Sunday as they face tough test against current league leaders Leicester City, who will to be looking to all but secure the title with a win on Wearside.
Despite Claudio Ranieri's side winning their last four matches, Borini remains confident that they can take points from the Foxes.
He said that they have to put "everything" into the game though to "make life hard for them".
Borini was one of a handful that were left frustrated on Saturday by Baggies keeper Ben Foster, who managed to pull off some great saves to keep the scores level, but the Italian said on another day it could have been a lot different,
He highlighted the fact that West Brom didn't have a "shot on target," but in contrast Sunderland had "two games worth of attempts".
He continued, saying that the team did "everything" they could and if it had been a "different keeper" or they had a "little bit of luck," they would have "won the game".
Sunderland will host league leaders Leicester City at the Stadium of Light on Sunday, April 10 with kick-off at 1:30pm BST.