Brighton have still to win a home league match in six attempts under Poyet but the Uruguayan said: "Very soon this will change. Our performance had everything apart from a goal. You can't ask for more.
"Football is about finishing and it's one touch, one penalty, one decision from the referee. These are the things that will change the situation."
Poyet chose to freshen up his strike force with Liam Dickinson partnering Chris Holroyd, and he was delighted with the way Glenn Murray responded after coming off the bench.
He added: "I'm really pleased with the reaction from Glenn Murray. We need that bit of competition. We've held the division's second highest scorers, got a clean sheet and in the end I'm very pleased with the performance."