Suarez departed the Camp Nou at the start of the season following six successful years after he was deemed surplus to requirements.
The former Ajax Amsterdam and Liverpool striker found a new home with Barcelona’s La Liga rivals Atletico Madrid and his 12 league goals has helped catapult the Rojiblancos to the top of the table, 10 points ahead of Barcelona, having played a game less.
"They took a very important decision which would not be easy for some people,” Poyet told Stats Perform News of Suarez’s summer switch to the Wanda Metropolitano.
"It was easy for El Cholo [head coach Diego Simeone], from what I know of him.
"Bringing in Luis Suarez as Barcelona didn't want him, bring him in now. And Luis went with his mentality, 'I will show you who I am'.
"A bit like a Uruguayan I am, 'You don't want me? Am I over? Let’s see!'.
"And this is blowing up LaLiga."
He added: "What it shows is that sometimes football players need something different, just something.
"It can be a different treatment or being tougher [on them]. But they need something to react to.
"He was low, not bad, but like the [Barcelona] team, he was low. He needed a new challenge and sometimes it is tough to get it in the same club.
"It can happen with arrival of a new manager, or signing a new player who becomes a rival of yours. There are different ways, but if it does not happen, it looks difficult.
"However, there is no doubt that joining such a special team like Atletico with such a special coach, similar character [to Suarez], you get it and he is showing that extra [effort] needed.
"Sometimes we all need to realise. Get out from the club and notice that you have to do something to change the situation.
"I was not doubtful on his performance, especially playing in that system and having that responsibility.
"I don't forget it that it was him or Diego Costa [playing] at the beginning, sometimes both together. But at the time, Costa had gone, with all the respect to other players, it was only Luis Suarez.
"That also gives him the responsibility on scoring 20 to 30 goals and Luis accepts it in a natural way."
