Wednesday's Premier League clash with Manchester City was postponed on safety grounds due to high winds around the Etihad Stadium. With Sunderland still in both cup competitions, a rearranged league fixture is just what Poyet does not want.
Sunderland - third bottom in the Premier League - faces Southampton in the FA Cup this weekend, still has 13 league games left and plays City in the League Cup final at the start of March.
Poyet admits it will be a tough end to the season, but felt the decision to call off Wednesday's match was the right one.
"The fixture position is the difficult part," the Sunderland head coach said. "We will have a lot of fixtures to play in a shorter amount of time now, because of our success in the cups. It will be difficult for us, and I can't imagine what it will be like for Manchester City, who are still in the Champions League and the FA Cup.
"We came across on Tuesday and prepared as normal. We had a meeting [on Wednesday morning] and set off for the game as usual. But it was very difficult to get to the ground. A journey that would normally take about 25 minutes took more than 40. It's true that we saw a few incidents outside, there were a few panels coming down towards our bus.
"Of course we were ready to play, and we wanted to play. But we have nothing to complain about. You don't know what is going to happen, but we need to be honest. It was a strong decision by the police, and we have to agree with that."
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