The bottom-of-the-table Black Cats fell behind early when Fernandinho struck for City but rallied thanks to a brace from youngster Connor Wickham which came in the 73rd and 83rd minutes.
"I think the first half we were even better than the second half, the only problem is we didn't score," Poyet told Sky Sports.
"At half time you need to convince the team at the bottom that we are the best team and to keep believing.
"The players tried their best and we were concentrating on making it difficult for them and trying to go forward and create chances."
The draw left Sunderland at the foot of the Premier League standings on 26 points, still five away from safety, with just five fixtures remaining.
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