Having surrendered all three points at Elland Road on Saturday following a 95th-minute equaliser, the Brighton manager admits he was relieved to have had a two-goal cushion at The Valley when Akpo Sodje struck an injury-time consolation.
He said: "We are lucky that we were two goals ahead. I have to make sure it doesn't happen again."
Having held Huddersfield and Leeds to draws in recent weeks, Brighton's form has belied their position among the relegation contenders.
Poyet added: "I don't know how many times people have said 'You deserved to get better against Norwich', 'You deserved to win against Leeds'. I'm pleased with the performance. That's our way. Good or bad? Like it or not? But when we play at that level, we can beat anyone."