It was a night to forget at the Samy Ofer Stadium in Haifa as Israel surrendered third position in World Cup qualifying Group G.
Having beaten their opponents by the same scoreline in November, Israel were expected to secure a comfortable win.
But they were given a lesson in finishing by a ruthless Albanian side who ended a run of three consecutive defeats, with goals from Armando Sadiku (2) and Ledian Memushaj.
Former Premier League star Berkovic said: “Elisha Levy has failed big time and should resign.
“He has built a team worth nothing. We saw a team that was timid, hesitant, lacking any character and most striking of all a sputtering team that Levy is failing to ignite.”
Israel captain Eran Zahavi admitted the team “were disorganised and did not come prepared properly for a home game”.
He said: “The responsibility is ours, what else can I say? We beat them well there and they got there revenge here.
“But it’s hard to play in June when we’ve all had a tough season. I hope we can make the fans happy again for the next home game.”
The result saw Albania leapfrog Israel on goal difference, seven points behind Spain and Italy who both won.
Levy said: “Until 2-0 we played well and were organised. Then I took more risks and we lost our way.
“Albania did to us here exactly what we did to them there. I didn’t think we could lose like this at home, but that’s football and we must look ahead.”
Israel return to action on September 2 when they host Macedonia.