Carvalhal instructed the Swans to make it difficult for the Reds by switching the play when the visitors pressed high.
"I made an analogy about this game [for the players]. I said Liverpool is a really top team and they are a strong team but they are a Formula One, but if you put a Formula One into London in the traffic at 4pm it will not run very fast. That's what we had to do against Liverpool, make them play the way they don't like," the Portuguese told Sky Sports.
"They have a principle that when they lose the ball they are very strong with pressing. We did these mistakes against Liverpool [before he joined] but today my players were ready for that, all the time my players one, two touch, all the time with support.
"When Liverpool put pressure on the sides we switched to the other to put them under the pressure. That's why we achieved more moments to get close to the goal.
"We had the fortune to score a goal. It's not exactly how we wish to play but the circumstances of the moment, we need the win.
"Since the beginning I told my players the most important thing is the belief. I try to give confidence to them, to give them belief. It's not just a question of belief, if you're not organised, you can believe a lot but you will not win any game."
Alfie Mawson scored the game's only goal in the first half following a corner and Carvalhal had identified the set-piece as an area Swansea could hurt Liverpool.
"We try to explore anywhere [to score against them]. We felt they have a lot of strong points but they have weak points and set-pieces was one of them," he added.