Tiago Monteiro and Rob Huff were the most outspoken about the Japanese tyre supplier's rubber after Monteiro, reversed grid polesitter Nestor Girolami and two European Touring Car Championship drivers picked up punctures during the opening race on the 15.8-mile German circuit.
Honda driver Monteiro, whose failure cost him the points, called it a "dangerous" situation while after practice on Thursday Huff said it was "unacceptable" for a world championship.
Yokohama technical consultant Ian Beveridge said the unique demands of the Nordschleife meant there was always going to be an increased risk on a standard race tyre.
"In free practice one there were some problems," he said.
"We then discussed that with the teams and they made some adjustments, and in free practice two, it was all OK, but I don't think anyone did a full race simulation.
"Then we came to race day, and the circumstances changed slightly more as we had hotter conditions, so the target's moved again.
"We only come here once a year, so it's a unique set of circumstances which we try to manage with the teams.
"All of us, the teams as well, are still learning.
"There are so many things that can catch the cars and the tyres out here; kerbs, rough parts, lots of compressions with the aero, long, long fast straights, which just produce a set of circumstances.
"I think we have a better understanding of what to do now.
"We've worked hard in the background to eliminate all these glitches, but we're not always successful."
Yokohama worked with the teams to provide a set of guidelines for tyre pressures.
It is thought all teams adhered to these this season, with Monteiro claiming Honda were even more cautious after Norbert Michelisz's Thursday puncture.
Huff went as far as to call for Yokohama to make a special Nordschleife tyre, but Beveridge said the championship's regulations did not allow this.
"There's two reasons," said Beveridge. "One, we can't under the regulations, as it's one tyre by the contract with the championship, so that's difficult to change.
"And even if we were to make a harder tyre, you'd lose performance, but in the same way that you'd lose performance by making this tyre run at a safe pressure.
"If we produced a stronger tyre, they'd just run it at a lower pressure to get the performance back.
"It's a decision not to make our settings compulsory.
"Only the FIA can do that really, and we're reluctant to do that as a championship as we want to keep the sporting element down to the teams."
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