The forward has been on the receiving end of punditry from Obi-Mikel, with the latter believing that Chelsea had to sign a top forward.
"(Kieran) Dewsbury-Hall, again, I have nothing against this player, it's not his fault," Obi-Mikel said on beIN Sport.
"It was the club who brought him to the club. He cannot help Chelsea.
"Madueke, who I thought played well at the end of last season, he didn't start the game, he didn't come on. You look to get the team better, (Mykhailo) Mudryk didn't help the team, he didn't come on. I think these players could have helped us.
"Again, we knew this problem from last season, to get a striker who will score goals. Jackson, he does a little bit here and there. We (Chelsea) need a top striker like we did back in our day.
"Didier Drogba, we knew, if you give him two or three chances he will score one. We see (Erling) Haaland today. The first chance he got, the way he took the ball, the way he finished. This is a top, top striker with Premier League experience. We don't have that and Jackson is not going to get us that.
"I talk and I know sometimes I talk and the Chelsea fans they see me passionately, it's because of how much I love the club. How much I want the club to succeed, how much I want the club to get back to where we were. We don't want to become a mediocre team who finishes 10th, ninth, every season.
"That's not who we are. We compete to win the Premier League, we compete in the Champions League. The more this goes on the more we start to drift into that situation whereby finishing 10th is comfortable for us. It's not comfortable for us. We want to get back to where we were. We need to start signing the right players and that starts by signing a top striker who can help us this season."
After scoring the opener in a 6-2 win over Wolves, Jackson took his chance to fire back at Mikel.
Posting on Instagram immediately after win, he wrote, "@mikel_john_obi shut your mouth don't talk s*** ,we are killing ourself (sic) for Africa (red heart, football, and world emojis)".
He also posted another time: "@mikel_john_obi have you got something to say ?? Promote you Young brother!! We need to be stronger All together . Show respect (fist emoji)".