The manager admitted he was in shock after seeing his team somehow only draw 4-4, having led 4-2 against David Moyes' Toffees with only eight minutes to go at Old Trafford.
"It was a throwaway, an absolute giveaway," said an aghast Sir Alex. "We just needed to see the game out and it was a travesty because some of our football was fantastic. The goals we scored were great goals. To give away four goals at Old Trafford in a home game like that which was so important to us is unbelievable. I can't believe it."
Expecting Manchester City to win at Wolves in Sunday's later fixture, Sir Alex told MUTV: "We've given ourselves a real task at the Etihad. We'll go there only three points ahead."
The performance against Everton was pure Jekyll and Hyde - with a wonderful attacking show from the likes of Wayne Rooney, Danny Welbeck and Nani let down by a poor defensive display.
"We've created our goals with really good football but I think they got their goals easily," reflected Sir Alex.
"Rooney and Welbeck were a real threat to Everton today, their combination play and understanding of each other was terrific. They should have got more out of the game than they did.
"Defensive lapses have cost us. In previous matches recently we've actually defended very well. But this was a bad performance defensively. It was a real blip for us today to get a performance like that. I think the goals we conceded were soft goals."