Poyet's men held his former club and league leaders to a goalless stalemate at the Stadium of Light and could be perhaps be considered unfortunate not to take all three points from an entertaining affair.
Sunderland spurned numerous opportunities to take the lead in the closing stages but, although Chelsea survived the hosts' late rally, Poyet is keen for his side to build momentum as they go into a week that sees them take on last season's top two in Manchester City and Liverpool.
"The players should go into these games now with a mentality of thinking we can win," Poyet said. "We can beat Man City and we can beat Liverpool.
"Chelsea did everything possible to win it - they passed the ball right, left, over the top, in the corners.
"They threw on every striker they had on the bench and tried their best. But we did something special and we have to take that into the next games."
Sunderland welcome City to Wearside on Wednesday before travelling to Anfield to face Liverpool three days later.
‘Newcastle’s board said I was over the hill, so I left and played 108 consecutive games and won the European Cup – not a bad way to answer that accusation!’: Ex-Magpies defender reflects on career highlight after proving former side wrong
‘Parma viewed him as the perfect replacement for Adrian Mutu, who’d left to sign for Chelsea. But Manchester United’s interest was much more concrete’: Cristiano Ronaldo's 2003 transfer details revealed by former Sporting director of football
