The Republic of Ireland international joined the Championship team on loan in January.
Obafemi scored twice in 12 starts, helping them to avoid relegation from the second division.
All I'm going to say is I'm building a culture and an environment at the football club," he said after it emerged that Obafemi had a disciplinary issue.
The standards are set by Neil Harris and Millwall Football Club. These are standards that I expect players to adhere to. Players will only be involved at my football club, when I'm in charge, if they hit those standards. It's all about culture and environment.
Michael has done brilliantly for us on loan and we're really thankful for his efforts. He didn't feature for us off the bench the other day he wasn't going to feature today. I'd rather play our own players who have trained impeccably.
Harris added: Michael was based around discipline but also around that we weren't not going to look to sign him in the transfer window, so no need to include him."
Of the comments, Clarets boss Kompany said: As a club, I don't think we're too pleased with the fact there was a big statement about it.
We always have a duty of care for the players we have but I don't want to get involved in other club's affairs."