Costello took aim at AFL players in his regular column in The Age newspaper on Wednesday, describing them as "working on the brand" when they took part in club-organised school visits.
In the wake of the scandal that rocked St Kilda over the summer, Costello went on to claim "any right-thinking parent would quake with fear to hear that footballers were coming to their daughter's school to give a little bit of inspiration".
Maxwell said on Twitter: "Love to see the community work Costello has done in his lifetime. Made an absolute fool of himself!"
Maxwell's teammate Harry O'Brien said: "Peter Costello should be more like his brother Tim who is cool & does better work for society.
"Peter Costello you seem so out of touch with this generation. You had your time in the sun... All AFL players can do is continue to be proactive in the community. The vast majority [is] positive. The media does not do us any favors."
Former Magpie and Gold Coast player Josh Fraser said: "Wonder if Peter Costello has ever seen the smile on a kids face when an AFL player turns up to do a clinic? What a goose."
AFL Players Association chief executive Matt Finnis leapt to the defence of his members on Melbourne radio station SEN.
"I think some of the accusations or the themes that are running through that article are really disappointing," Finnis said.
"I think the reality is that when players go to schools or to Auskick centres, they're going there because there are young people all over Australia who are wanting to play AFL football and what they want to do is meet their heroes.
"They want to engage with them and I think one of the strengths of our game is the ability of the public to engage with our players and for young kids to do that.
"I think that to question the motives of players engaged in that kind of activity is really disappointing."
While outraged by the article, Finnis said the AFLPA would not be looking to take the matter further.
"I'm not sure that Peter holds any position of relevant responsibility in terms of government policy," he said.
"So I'm not sure to what extent we need to try and respond through formal channels apart from making sure that people understand that what the players do is done for the right reasons."
