A 2-1 win against Sheffield United on Monday night confirmed Burnley's promotion from the Championship. Parker pulled off achievement at first attempt, having replaced Vincent Kompany last summer.
He said afterwards: "The ambition and target at the start of the season was to get back to the Premier League.
"We've managed to do that so I'm hugely proud of the squad.
"It's come down to real, pure commitment from every one of the players, their dedication and the sacrifice that they've made, that leads us to this point."
Emotional for Parker
Parker admits it was an emotional night for him, personally.
He continued: "I explained to the lads there is emotion from me because I see the commitment that everyone has brought.
"We live in a world where you win or you lose and you get judged and at the end of the season you're either promoted or not and that's how quickly people will judge it.
"I'm just delighted that all that work, all that effort, all that sacrifice has been worth it and people can see it. The facts are if you don't get promoted people can see it."