Out-of-contract at season's end, Allen's position as leader came under question after sitting down with Mitchell to discuss his future just a day after a poor performance in the winless Eagles' western derby defeat to Fremantle.
But the 26-year-old has been backed by the club to remain in his role partnering Liam Duggan despite saying he was "embarrassed" and "ashamed" by his actions.
Allen fronted the media in Perth on Thursday alongside West Coast football boss John Worsfold.
"I feel remorseful towards our fans, our playing members, supporters, staff ... I'm incredibly remorseful," Allen said.
"I'm going to continue my role as co-captain alongside Liam Duggan this season.
"In conversation with people at the footy club, everyone feels like it's the right thing to do.
"I still am really confident I'm the right man alongside 'Duggo' to take this club forward and achieving some real progress and success this year."
Allen admitted he had turned off his phone after news broke on Tuesday of his meeting with Mitchell.
He is being heavily pursued by Hawthorn and reigning premiers Brisbane as one of the AFL's most in-demand free agents.
The Lions, who had 12 months of warning on Joe Daniher's post-grand final retirement, have long had Allen in mind to be the new key of their forward line.
Hawthorn poached premiership defender Tom Barrass from the Eagles during the off-season and have also been linked to West Coast's No.1 draft pick Harley Reid.
"As a leader, the best thing I can do is to play well on field and lead the boys by example," Allen said.
"I clearly haven't been doing that.
"I just want to play some good footy for this great footy club that I've loved growing up and still do love.
"Clearly, I wouldn't hold it against them (the players) if there was some anger or frustration towards me.
"They've been incredibly supportive for me this week and so far this year.
"I addressed them (on Thursday morning).
"I just felt quite embarrassed and ashamed in front of the boys.
"Everyone here is working as hard as we can to achieve success and to get better every day.
"And clearly my actions have become a distraction this week, which is exactly what I don't want for this playing group."
Worsfold indicated he would have preferred the meeting had not become public, but said free agency had dramatically changed how clubs and players approach the trade market.
"This is not a unique situation, but the public nature of it, we've all acknowledged isn't great timing when the team is struggling on field and trying to build our new identity under a new coach," Worsfold said.
"It didn't work out perfect, but we learned from that."
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