The winning, and only goal of the game, came from David Lopez on twenty minutes, and Poyet said at the final whistle: "It was a massive win for different reasons. We did not play fantastic and Burnley were a difficult team to play against, but we worked very hard for the three points which is very pleasing.
"Technically we were not great as a team today but we won the game and throughout the season that is very important. We have to make strong decisions and that makes us better as a team.
"I've never made such a defensive substitute as bringing on Gordon Greer for Vicente but there are reasons for that and it was because we had to make sure we got the win. To win games like this is very important.
"As a team we put in a performance to show that we can win a game somehow, when we need to. We are in the top six but we will have to see what Middlesbrough do. We look at it day by day and we are very happy with the way it's going."
Poyet heaped praise on his match winner and his match save, goalkeeper Tomasz Kuszczak. Of Lopez, the goalscorer, he said: "He is a different player and I always try to play him. He's calm, he hits the ball very well and he gives us a lot of options.
"His technical ability is at a very high standard. Because of his ability he scores some very important goals and he showed that again today. He and Wayne Bridge were two of our best players today, that's why David is playing and Bridge showed one of the best performances for a full back at this club."
And his goalkeeper: "We knew that the quality was there with Tomasz. He's had a few difficult moments this season but he has reacted very well. Casper Ankergren and Peter Brezovan encouraged him a lot too and today he made a spectacular save with his left hand. It was a key moment in the game."
Sean Dyche, who has now seen his team go on a run of five games without a win since beating Millwall five weeks ago, felt the Clarets were hard done to in coming away without even a point.
"Today I can't ask a lot more of the players. To give that type of performance down here, dominate the ball and create chances, it's beyond me how we came away with nothing.
"We had a sticky ten minutes in the first half when they had us on the rack and the game could have gone away from us, but other than that I thought we were very good.
"We've pushed hard, created chances and been denied by a great save from the keeper, had one cleared off the line and Charlie has just missed with two headers.
"It's just that moment of clarity in taking the chances, but we have another positive performance to come from it and I have just said to the players that if you carry on playing like that, you win football matches.
"Football doesn't always play you back immediately, but it does over time and the last few performances have been very good, particularly in the second half today."
He added: "It's a concern if you are not creating chances. You can't bluff yourself by saying how well you are playing if you are not creating them, but if your play is productive you don't have too many worries.
"Would I take a scruffy, ugly 1-0? Of course, but the future looks bright when we are performing like that."
Just as Poyet singled out two players, Dyche had positive words from rookie defender Kevin Long who was making just his third Burnley start.
He said: "Kevin was absolutely outstanding and that bodes well for a young player who is still learning his trade. I rarely single out a player for praise, but he was outstanding. He's a young man coming to a venue like this and it's a big occasion for him.
"He was up against big players today with big reputations who have cost a lot of money, but he didn't look fazed at all, so we have some real positives.
"You look at this run we are on and wonder how we haven't won a game. It's amazing but it will come."