Sunderland won promotion back to the second tier after four long years in the third tier of English football, the 2-0 Wembley win over Wycombe Wanderers securing promotion in the League One play-off final.
The club are yet to sign any new players ahead of the new season, however, new deals have been agreed with key players including Bailey Wright, Anthony Patterson, Patrick Roberts and Lynden Gooch.
Poyet, speaking ahead of the new season to the Lord Ping website, said: “I'm delighted that Sunderland are back in the Championship, but they need to make sure that they don't go crazy by expecting to reach the Premier League.
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"Alex Neil was outstanding and done so well.
"There's a big gap between League One and the Championship and so they need to make sure that they know their objectives.
"Sunderland need to be realistic and just focus on staying up, then they can re-evaluate and aim for certain things.
"Sunderland can't afford to be unrealistic because there are so many strong teams in the Championship.”
Speaking after Wright signed his new deal, boss Alex Neil said: “Going from League One to the Championship is a big step, but we wanted to keep that core together and retain our key performers from last season.
"We know the leadership qualities that Bailey has, and he has played in the Championship before so he adds experience, but his influence on other players can’t be underestimated.”