The former head of the army said that the West may "need to put some people on the ground" in Iraq.
Asked if that meant UK forces, Lord Dannatt told BBC Radio 4's Today programme: "The United States in the lead and us in support. We all bear some responsibility."
"The breakdown in society in Iraq post-2003, we have some culpability for that and so it is difficult for us to say 'Not our problem'."
He added: "It may be unpopular but it might be the right thing to do."
Kurdish Peshmerga fighters have emerged victorious in the battle for Mosul Dam, but the question is - what will their next move be?
An ITV News team at Mosul Dam was with victorious Kurdish Peshmerga fighters at the complex earlier today.
ITV News joined a Kurdish unit fighting Islamist militants near Irbil and found them using tanks from the 1950s and short on ammunition.