When it was announced on Thursday that, after 22 years, 60-year-old Haug will not be with the German marque in 2013, some sensed the hand of Mercedes' new non-executive chairman, triple world champion and Austrian great Lauda.
"I want to state strongly that this was a decision that the board and I reached by consensus. Niki had absolutely nothing to do with it.
"We have respected each other over the years, and this changes nothing," Haug told the news agency SID.
He hinted that Mercedes' failure to properly succeed since forming its works team in 2010 was a reason for the split.
"We have had success in the past three years, but not enough consistently," said Haug.
Niki Lauda told German television Sky: "I was just as surprised as anyone about Norbert.
"For me personally, I'm sorry about it. I have always had a very good relationship with him and would have very much liked to have continued to work with him."
Michael Schumacher, who is returning to retirement in 2013 after three seasons with Mercedes, also sounded disappointed with the decision.
"This step represents a major turning point," the seven time world champion said on his website.
"His departure will tear a big gap in both our sport and our team."
German motor racing federation president Hans-Joachim Stuck is quoted by Speed Week: "Norbert has also had some health problems, perhaps that played a role."