Former England Women's star Aluko aimed comments at Wright this week over his work as a pundit in the women's game.
Ian Wright says he cannot accept Eni Aluko's apology
Aluko suggested men need to be aware of blocking opportunities for female pundits
The pundit later apologised for mentioning Wright's name
Aluko spoke about importance of making sure female pundits were not blocked by men, suggesting there is a "finite amount of opportunities" and "men need to be aware of that".
She since apologised to Wright after public backlash, but the former Arsenal star is unable to accept.
He said in a video on Instagram: "I'm very disappointed by what Eni has said.
"She knows how I have helped her and supported her publicly, and I know the previous conversations she's had with me and my management.
"I've seen the apology on social media, but I can't accept it, but I also want to move on from it. I don't need any further social commentary directed at anyone."
The pair have worked together for ITV in the past, including during the 2022 World Cup in Qatar.
Wright, 61, acknowledged the negative role men have played in limiting the women's game in the past, and he said he does not take his role as a pundit for granted.
He added: "The thing about where the women's game is, it isn't about me - it has to be about the collective.
"Because of the past, we know the men blocked the women's game for 50 years, because of the past we know the game has serious systemic challenges, and it's going to take everyone to help fixes.
"So for me, I always give back to the game, it's given me so much.
"It's never bothered me about who's playing the game, as long as they're playing the game. if you know my story you'll know how much football means to me.
"We are the country that invented modern football, so we have a responsibility, to lead the way in women's football
"We men are the ones that banned women's football for 50 years, so we have to hold that one. I need to say to everyone who has spoken about it publicly and showed love and support, I say thank you
"It's something I do not take for granted."
Aluko, 38, apologised to Wright over her comments, admitting it was wrong for her to mention his name while making a broader point about the women's game.
She said: "In my interview with Woman's Hour this week, I was trying to make a broader point about the limited opportunities for women in football - whether that's in coaching, broadcasting or commercial space - and the importance of creating more space for women to thrive on and off the pitch.
"But it was wrong for Ian's name to be raised in that conversation, and for that I sincerely apologise.
"I've known and worked with Ian for many years and have nothing but love and respect for him."
Wright has been a big advocate of the women's game for a number of years and shown his support in a number of ways.
He made an incredible gesture to Stoke City defender Kayleigh McDonald after she suffered a ruptured ACL was forced to set up a GoFundMe page to raise funds when the club refused to pay for surgery.
Stoke eventually backtracked - largely thanks to Wright, it has been revealed, as he paid for a sports lawyer to advocate for McDonald.
And when the club pulled funding for her rehab at the end of last year, Wright started paying for it out of his own pocket.
The defender revealed that her rehab costs around £1,700-a-month.
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