United earned a 1-1 draw in the first-leg of their Champions League round of 16 tie.
Martinez told Absolute Radio: "Well I think it's first and foremost they went through the hardest test that they had which was going to the Bernabéu, I think it was great for the Premier League as a whole, obviously we were watching it from Spain and you could hear the comments.
"And they expected a team from the Premier League that couldn't cope with the tactical element of a Spanish team and I think at the end of the game it was an incredible respect for the performance of Manchester United, of knowing what to do at every stage, using players like Van Persie, Welbeck and Rooney in a different role which surprised Real Madrid.
"And all in all taking the leg, or probably the decisive minutes into Old Trafford which overall was an impressive performance against a team that they'd been really strong at home, where they'd been suffering Real Madrid is away from home. But being the best team on the counter attack in world football still gives them hope but I do see now Manchester United are slightly favourites in the second leg."