Real, who were humiliated 6-2 at the Bernabeu by Pep Guardiola's treble-winners in the last 'clasico', fell to a 56th-minute volley from Zlatan Ibrahimovic, but still made life tough for the champions.
"It has been an intense and attractive match with two ambitious teams," Valdano told Canal Plus television.
"We deserved to have little more luck but the team showed enormous maturity in a difficult stadium."
Real's expensive squad were leaders going into Sunday's game but had been heavily criticised in local media for failing to entertain despite possessing players of the calibre of Kaka and Cristiano Ronaldo.
"We are pleased with the way the players conducted themselves. They put in a huge effort and put on a good performance," Valdano added.
"This game should ease the criticisms of us, as it proves the side are making progress and that we have the players to compete at this level."
Coach Manuel Pellegrini was not as positive as his boss as he expressed his frustration at having let 10-man Barca off the hook, and he explained why he substituted one of his most dangerous players, Ronaldo, midway through the second half.
"(After his ankle injury) He wasn't fit to play more than an hour. It wouldn't have been wise for him to play more," the Chilean said.
Barcelona's victory put them two points clear of Real at the top of La Liga, and their coach Pep Guardiola was full of praise for his team.
"It's always difficult to play Real Madrid and even more so when we were cast as clear favourites," he said.
"Real played a great game but we didn't lose our cool. We didn't play very well in the first half...but the fans enjoy it when we win this way as well, showing character and determination."
