The Red Devils took the lead through Danny Welbeck before Cristiano Ronaldo's header levelled the tie, and the Scot believes his side are capable of claiming 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 counter-attacking 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 at Jose Mourinho's Madrid, 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.
|RONALDO STORMS MANCHESTER|
|6/1||Real Madrid are 6/1 with Coral to win the Champions League|
Sir Alex praised former player Cristiano Ronaldo, who spent six years at Old Trafford before moving to Spain and scored the equaliser for his side with a superb header.
"What a header [from Ronaldo], unbelievable," he added. "You can't stop that. The leap, the spring and holds himself in the air and unbelievable power in the header.
"I came in at half-time and said to Patrice, 'Are you not challenging for that?' and I saw the video and thought, ‘God, what was I talking?’
"I thought we did very well. I think it was difficult for Cristiano playing against us, his old team.
"A lot of emotions attached to it for him because he spent six great years with us. But he's still a big threat for them. When he gets the ball you are praying more than anything."