Kulusevksi came on for a 20-minute cameo but said in a postmatch interview that he was shocked that he did not get to start, and Andersson's surprised reaction to the criticism provoked a strong response from Ibrahimovic, Sweden's record goalscorer.
Ibrahimovic expressed his frustration with a Twitter post on Sunday which read: "What a damn joke. Further proof. Incompetent people in the wrong positions smothering Swedish football."
The post included a link to an article from newspaper Aftonbladet which featured Andersson's postmatch comments.
After scoring 62 goals in 116 games, Ibrahimovic retired from international football following Sweden's exit from Euro 2016.
When asked if he had been given enough time to show what he could do after coming on for Sebastian Larsson, Kulusevski replied: "No, no, I don't think so.
"I was shocked. It felt really, really good in training. But unfortunately, that's how football is."
"I haven't spoken to him afterwards but if he has said it then that is clearly his opinion," he told reporters. "We'll have to talk about it.
"I haven't experienced him as being very shocked. He has done well in the training session, as have many others."
The 57-year-old coach said it was likely that Kulusevski would see more playing time when Sweden host Portugal in their next Nations League game on Tuesday at the Friends Arena in Stockholm.