The Scot is bullish on his side's prospects for advancement after leaving Madrid with an away goal and an even scoreline
The Red Devils took the lead through Danny Welbeck before Cristiano Ronaldo's header leveled the tie, and the Scot believes his side is capable of taking victory against the Spaniards.
"It's very open," Sir Alex told Sky Sports after the game. "I think we'll score at Old Trafford. We know they are going to be a tremendous counterattacking team, we know that. I've seen that when they played Manchester City at the Etihad Stadium, in the first half, they dominated the game. We have got a big task on our hands, but it is definitely within our grasp."
Manchester United created a number of chances in what was a pulsating game away to Jose Mourinho's Real, and Sir Alex has praised his side's efforts in what was an intimidating atmosphere.
"I think, all in all, we created a lot of chances in the match, we've played some good, attacking football at times but not got the possession that we should have had," he said. "I think Real won possession without question, they are at home, it is a difficult place to come to but I have got to be pleased that the players dug in and got a result to take back to Old Trafford with a great chance.
"I think there were a lot of incidents in the match, a lot of chances at both ends. David De Gea has had two or three great saves but we have missed two or three great chances ourselves. The goalkeeper has made a great save in the last minute and a fantastic save from Van Persie, which hit the bar. So there were a lot of incidents that made it a really interesting game."
Follow GOAL.COM USA on