The French capital club, who have never been champions of Europe, enjoyed most of the possession against the 10-times winners but were toothless up front and had to be content with a share of the points.
After three games they are level on seven points with Real in Group A but face the Spanish giants away in their next fixture so are unlikely to top the section.
PSG, who have benefited from massive investment from Qatari owners QSI since 2011, have been eliminated in the quarter-finals in the last three editions.
They fell just short in 2013 and 2014, being eliminated on the away goals rule by Barcelona and Chelsea, and last year's 5-1 defeat on aggregate by Barca had been preceded by a superb performance when they knocked out Chelsea despite being down to 10 men in the return leg.
Blanc is well aware that winning the Champions League is a long-term project and PSG, who were only founded in 1970, may just be at the beginning of the journey.
"The PSG project is only four years old, and we got where we are fast," the former France coach said. "It's already a good sign that we were competitive against Real.
"We will need time to take another step."
Despite only drawing with Real, Blanc said his side have already shown their pedigree in the competition.
"We were being told that we needed to beat Real to send a signal to Europe," he said.
"But we already have references. We beat FC Barcelona and Chelsea, and all the European clubs have that in mind."
PSG enjoyed 60 percent of the ball on Wednesday but that did not translate to more scoring opportunities as Zlatan Ibrahimovic, Edinson Cavani and Angel Di Maria failed to ignite.
"All your players need to be at the top of their game if you want to compete with one of Europe's finest teams," said Blanc.
"The aim for the club remains to win the Champions League, but you have to remember the project is only four years old."
(Reporting by Julien Pretot; Editing by Martyn Herman)
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