The Stadium of Light outfit have endured a torrid season, and sit bottom of the Premier League with just 14 points from 20 matches.
Sunderland have been boosted by two morale-boosting victories in cup competitions, however, with a 3-1 triumph over Carlisle United in the FA Cup last weekend followed by a battling 2-1 win over Manchester United in the League Cup semi-final first leg on Tuesday.
Johnson was a standout performer in both of those fixtures, including coming off the bench to win the penalty that secured Sunderland the victory over United.
It represents an upturn in fortune for a player who has struggled for form this season, and Poyet believes the England international is crucial to the club's chances of survival.
"We have to find a way to get the best out of Adam because I understand that has not been the case so far," Poyet said.
"Adam Johnson needs to make the difference.
"He's that type of player - a player who has the quality to change the match for you in a single moment - and we need him to be making the difference for us in games.
"If he's not doing that, then it is my job to change that and to help him."
Meanwhile, Johnson himself concedes his chances of being named in England's squad for the FIFA World Cup in Brazil this year are all but over.
The 26-year-old has played 11 times for England, but has not featured for the national side since August 2012, and the former Manchester City man does not expect to be in Roy Hodgson's plans despite fellow winger Theo Walcott's likely absence with a knee injury.
"I'm probably too far away now," Johnson told the Daily Express. "His (Hodgson's) mind is made up.
"He has used 30-odd players and I haven't been one of them, but I won't give up. Theo Walcott is quite a good friend of mine so it wasn't nice to see that happen to him but you have to take your chance.
"It's always going to be in the back of your mind to go to a World Cup having been involved with England for a few years until I signed for Sunderland. It's still difficult, but you never know, stranger things have happened."
