The former Blackpool and Swansea star struck his first goal for the Seagulls in added time to earn Poyet's side just their third home win from their last 12.
"He has showed what he is capable of," said Poyet, who has handed Dobbie only two starts this season. "I told him when he came on that this was his chance. We needed quality and he delivered it.
"Hopefully Dobbie will now relax and make it more difficult for the manager. The way football is nowadays, we don't wait for people to adapt. We want a hat-trick from new players straight away.
"Stephen had two or three chances when Craig Mackail-Smith was out injured and he didn't score, but it's not that easy. Obviously he wanted to score as soon as possible and I am delighted he is now off the mark.
"I hope this win can be a turning point. It's up to us. We have got two difficult away games now against Wolves and Huddersfield, and we must keep believing.
"In the second half it was all about us. We had 32 shots and scored one goal. But the key to it was we didn't concede a goal so we won the game. If you don't concede it gives you the chance of winning."