PSG were the better side prior to Nacho's 35th-minute goal and continued to threaten thereafter, but failed to force a deserved equaliser in the Group A clash.
Di Maria had the best two chances of the second half for PSG, forcing a one-on-one save from Keylor Navas just after half-time before hitting the crossbar with a free-kick late on.
Blanc lauded the Argentina midfielder – who signed from Manchester United for an estimated €63million at the start of the season – for upping his game against his former club.
"Just like the rest of the team, Angel dramatically raised his performance level compared to recent matches," the coach told reporters at the Santiago Bernabeu.
"That result shows how football can turn out sometimes. But I think in a game like that – even if we didn't get the points we came for – we have to see the positives.
"After the first leg [which was drawn 0-0 at Parc des Princes a fortnight ago], some people said that we are not able to compete with the tempo of Real, but we showed that we can endanger any team tonight.
"Compared to our last game against Madrid, our offensive movement was much better. Real Madrid didn't come close to walking all over us.
"We have to build on this; it bodes well for the future. I'm pretty satisfied on the balance of both games against Madrid."
PSG, who have a 10-point lead in Ligue 1 already, have a four point cushion in second spot in the group and look primed to join Madrid in the last 16.