Despite surviving a couple of scares in defence in the opening stages of the Champions League Group C clash, the Reds looked to be cruising to victory after two goals in a minute from Danny Welbeck put the home side 2-0 ahead, after 17 minutes.
The latter netted a second from the penalty spot 14 minutes from time before Ashley Young stole in at the far post to head home an equaliser in the final minute.
"I feared the worst," Sir Alex told MUTV afterwards. "Some our forward play in the first half was absolutely fantastic, but there was always that lax attitude at the back and they were creating chances.
"We were fortunate not to have lost a couple of goals before half-time. Equally though we could have scored four or five.
"We said to the players at half-time you can make this game easy or hard for yourselves. And we made it hard. The attacking instinct in the team meant we got really exposed in midfield and at the back.
"There's sometimes a tendency to enjoy that [attacking] part, particularly at home, but in big game situations you would anticipate better defending and better concentration.
"Yes, we've been making changes to the back four, too many times maybe at the moment, but nonetheless they can do better than that."