The 55-year-old was sacked on December 22 with Palace placed 17th in the Premier League having won only one of their last 11 games.
"Looking back, I sat down with Steve in the summer and we decided we wanted to take the club forward," he told the Times. "We made changes but I definitely have the view we didn't change the squad enough.
"We brought players in but I think we should have done more. That was compounded when we thought we had good cover at left back, not thinking Pape Souare would be in a car crash. That was a big mistake not getting cover in one or two areas.
"Sometimes as manager you do get loyal to players. They kept us up, we got to the cup final. I couldn't fault their attitude but we didn't have a balanced team.
"The players I've had, I think I've largely got the maximum out of them but maybe you can't keep going for maximum. Maybe my loyalty gets in the way a little bit. I have been loyal to a fault with some. That's just a trait I have. Something I have to keep an eye on."