Sky Sports' Graeme Souness described Man United's display in Madrid as "faultless" - but told Sir Alex Ferguson's men to expect a strong response from Real at Old Trafford.
The Premier League leaders snared a potentially crucial away goal as they drew 1-1 with Los Blancos in the Bernabeu in the first leg of the Champions League last-16 tie on Wednesday night.
Souness - who won the European Cup with Liverpool in 1978, '81 and '84 - praised United for their defensive resolve and ability to create chances, but thinks Spanish heavyweights Real could thrive when they trek to Manchester for the second leg on Tuesday, March 5.
"United will see this as a very good night's work and it bordered on faultless," said the Scot.
"They played a lot of the game without the ball and David de Gea had to make saves, but they were disciplined throughout, carried a threat and on another night Robin van Persie could quite easily have had a hat-trick.
"However, Michael Carrick, Phil Jones and Shinji Kagawa competing against Xabi Alonso, Sami Khedira and Mesut Ozil is a mismatch (in midfield) and with United wanting more of the ball and to be on the front foot at Old Trafford, that makes Madrid a very dangerous team, especially with Cristiano Ronaldo on the break.
"United's game plan of containing Real and hoping Van Persie, (Danny) Welbeck or (Wayne) Rooney got a goal worked to perfection, but it will be a whole different ball game second time around.
"It is sometimes easier to play away from home in European football and as Ferguson is cute and has been around the block, he knows this tie is far from over."
Former United star Ronaldo netted a bullet header at the Bernabeu to level matters (30) after Welbeck had nodded the visitors in front (20), but Sky Sports pundit Jamie Redknapp reckons Ferguson's charges negated the Portuguese's threat well throughout the game.
And the former Tottenham and Liverpool player - who claimed that referee Felix Brych "bottled it" when he did not dish out a red card to Real defender Raphael Varane after he seemingly fouled a running-through-on-goal Patrice Evra - now expects the Red Devils to secure a spot in the quarter-finals.
"Ronaldo is one of the best players in the world and you have to accept that you are going to get beaten at times - but I think United dealt pretty well with him as a whole," said Redknapp.
"The way they set-up helped that; Jones and Carrick played in central midfield and didn't move very far and while Rafael's head was spinning early on - it was like he was in a tumble dryer - he recovered and did his duties well in the second half and Ronaldo drifted out of the game.
"I think Ronaldo might get more space at Old Trafford and so United's attention to detail when they haven't got the ball will have to be (really good).
"But I make United favourites as Real have lost eight games this year and they've all been away from home, so there is certainly a chink in their armour."
United custodian De Gea made a series of saves in his birth city of Madrid, including tipping a Fabio Coentrao strike onto the post in the first period and denying the Portuguese left-back again in the second half courtesy of an unorthodox stop with his feet.
Erstwhile United goalkeeper Peter Schmeichel saluted the performance of the 22-year-old, but says he was disappointed by what he witnessed from Real, who last won Europe's premier club competition in 2002.
"There were some great performances by United players," said Schmeichel, who tasted Champions League glory with the Manchester giants in 1999.
"Jonny Evans was fantastic at the back and justified his selection, Rio Ferdinand played really well and Carrick was fantastic, too.
"But the man of the match by a long way was De Gea; he was very solid, his first save (from Coentrao) set the team up as going 1-0 down would have made their task harder, and while some of his other stops might not have been the hardest, the important thing was that he made them.
"Man United have evolved into a very good Champions League side and since Christmas they have been very solid defensively, while I think Real were exposed (on Wednesday) and they showed they weren't able to control a game; they weren't able to find the gaps (with passes)."
Schmeichel added: "I think this will be a big test for Ronaldo at Old Trafford; I came back and played there with other teams and it wasn't easy as you have mixed emotions.
"You want to do well for your team but you have memories of the playing for the other club. There is a chance he might try too hard."