Champions City had the opportunity to close the gap on leaders Chelsea to just one point heading into the new year when they hosted Burnley on Sunday - as Jose Mourinho's men had drawn 1-1 at Southampton in an earlier kick-off.
However, Manuel Pellegrini's men surprisingly surrendered a two-goal lead to draw 2-2 with the strugglers, meaning Chelsea remain three points clear at the summit.
Sunderland head coach Poyet believes that the setback could stir City and is well aware that his team will need to play to their maximum potential to leave the Etihad Stadium with three points.
"Now they [City] have drawn and it's a little bit of a wake-up call, so I don't know, we will see," he said.
"We know Manchester City, we know how good they are, we know the quality they have got. We need to make sure that we are good on the day."
Poyet remains without full-backs Anthony Reveillere (calf) and Patrick van Aanholt (shoulder), while midfielder Liam Bridcutt is on the sidelines after suffering a concussion in Sunderland's 0-0 draw at Aston Villa on Sunday.
Midfielder Sebastian Larsson is expected to shake off an ankle complaint in time to feature.
City may have slipped up against Burnley, but prior to the meeting with Sean Dyche's men they had clocked up seven straight league victories.
One of those successes came against Sunderland on December 3, with Poyet admitting his team could not cope with the quality of Sergio Aguero - who scored twice in a 4-1 away win.
The Uruguayan will not have that problem to contemplate this time, though, as the Argentine striker remains sidelined with a knee injury.
Captain Vincent Kompany (hamstring), striker Edin Dzeko (calf) and centre-back Matija Nastasic (muscular injury) are also out for City, while midfielder Fernando is suspended having clocked up five yellow cards.
Pellegrini - who confirmed that midfielder Frank Lampard is able to play despite the impending end of his loan deal from sister club New York City FC - has enjoyed a 2014 that brought a Premier League and League Cup double last season.
And he is hoping to start 2015 in the right fashion against Sunderland - who they defeated in the League Cup final.
"In general it  has been successful," he said. "We have the next five months now to continue to improve the way we play.
"I hope we start the new year winning three points. Sunderland are a good team with a good manager. They have strong players."
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