The former Ipswich Town man scored five Premier League goals in April to help Sunderland maintain their top-flight status.
Having previously failed to establish himself under former managers Martin O'Neill and Paolo Di Canio, Wickham was offered the opportunity by Poyet following loan spells at Sheffield Wednesday and Leeds United.
Wickham scored eight goals in 11 games during his most recent spell at Hillsborough and feels it gave him the chance to tie down a place at his parent club - something he is eager to build on.
"It was a personal choice (to go on loan), I asked (Poyet) go to out," he told The Independent.
"I kept pestering and pestering him and asking, 'if I'm not playing, can I go?' Thankfully, in the end, he did let me. Sometimes you have to take a step backwards to go forwards.
"It stood me in good stead and propelled me towards the first team at Sunderland.
"I need to make sure that I'm in the team every single week next season and prove to people that I am no flash in the pan. Ever since my debut (April 2009) I have wanted first-team football.
"It's like a bug, you can never beat the feeling of walking out in front of 50,000 people and scoring. It is something you get addicted to."
Having kept Sunderland up and guided them to a League Cup final appearance, Poyet has been linked with a number of job opportunities elsewhere.
However, Wickham wants the Uruguayan to stay, and backed the squad to produce a better performance next season.
"Of course, we all want him to stay," he continued.
"Training is good, he is very down to earth, you can always talk to him. He is open to suggestions from players.
"He knows exactly what he wants and is very organised, it took us until the last five games of the season to show it."
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