Brighton, who had thrown away leads in each of their previous three Championship outings, were fortunate to escape with a point at the Amex Stadium as Aaron McLean and Robert Koren both went close with shots against the crossbar in the second half.
Poyet said: "We were much better today. Hull were tricky opposition and it was great to get a clean sheet - that's the main point."
Former Leeds keeper Casper Ankergren produced several fine saves and Poyet felt that it was the Dane's best display for a month.
He added: "Casper needed this performance. It certainly went through my mind to drop him, but that could be said about seven or eight other players."
Poyet is not too concerned about Brighton's winless run, although he is calling on his players to find the consistency which took them to the top of the Championship in September.
He added: "Everyone has seen Brighton play against Liverpool and Leeds on the television and thought that we are a very good team. But there are some very good teams in the Championship.
"Hull made it difficult but I was pleased with the way we tried to win the game all the time.
"I'm the sort of person who will never be happy with a point at home, but getting a clean sheet was very important for us and a good base to build on."
The Seagulls produced one of their best opportunities early on when defender Lewis Dunk headed wide at the far post following a cross by former Spanish international midfielder Vicente Rodriguez, and Poyet admitted: "Had that gone in it would have changed the game."
Hull manager Nigel Pearson hit back at critics who accuse his side of not playing attractive football.
He said: "I hear on a few occasions that people say we are not attractive and are a bit dour, but is a load of rubbish.
"This was a game when both sides tried all out to win. I was delighted with our performance, some of the quality of our passing was excellent and we deserved to win the game."
Hull, now unbeaten in seven games, have been lacking in goals this season but Pearson insisted he was not worried.
He said: "I'm very confident we will be a potent force up front.
"Brighton had a spell when they made their substitutions that they took the initiative, but our players stuck in really well throughout.
"We were very disciplined but still played a very offensive game and our players all performed very well."
Pearson is convinced some of his young players will be stars of the future.
He added: "We've got a very young side but have excellent players who can give the club long service and will be worth a lot of money.
"We want to continue to develop them and the spirit at the club is outstanding compared to a few months ago. I'm very pleased with the way things are developing."
Source: Team Talk
Source: Team Talk