Armenia have endured a difficult World Cup qualifying campaign, failing to win a game since March and currently sitting fifth in Group E.
"Problems are everywhere," Mkhitaryan is quoted by the Manchester Evening News as saying.
"We must do everything to ensure that this does not happen again in the match against Kazakhstan. There are no words.
"It was a shameful defeat. I am the captain of the team, and I undertake all responsibility for defeat from Poland."
Armenia, who cannot go higher than fifth place in their group, head to bottom side Kazakhstan for their final World Cup qualifier on Sunday.