The Euro 2004 winners have scraped one point in four Euro 2016 qualifiers under Ranieri, scoring one goal and conceding five, culminating in last night’s historic 1-0 loss.
“Following this devastating result for the national team, I take full responsibility for the most unfortunate choice of Coach, which has resulted in such a poor image of the national team being put before the fans,” wrote HFF President Giorgos Sarris on the Federation website.
“The governing board will convene and take responsibility among all the members to make the necessary changes needed to avoid a repeat of such an embarrassing night.”
There are now reports ex-Italy and Republic of Ireland manager Trapattoni will replace Ranieri at the helm.
It was the first Faroe Islands victory since 2011 and 63-year-old Ranieri admitted to being flabbergasted.
“I have no words to explain what happened,” he said in a post-match Press conference.
“We all wanted to record our first victory in the group. But the Faroese deserved to win as they created more chances to score. Only hard work can get us out of this situation.
“When the qualifiers started nobody believed we would find ourselves in this situation. We were wrong in believing that was a straightforward group for us. All defeats hurt equally, but we must leave results in the past and work our way out of this situation.
“We are last in our group because that is what we deserve. The Coach is always responsible for that. Back in September, most of my players were low on form following the World Cup, but this week during training I saw my players very lively and motivated. That’s why I am very surprised about the result.”