The Formula One team's non-executive chairman, himself a triple world champion, refused to blame Hamilton and told reporters he would have done exactly the same in the circumstances.
"The team was under enormous stress," he said of an incident that became a major talking point after Hamilton raced from the pitlane to third place while Rosberg started on pole and finished fourth.
"Mercedes was used to being in the lead and racing against each other. This race, with the safety car at the beginning and wet conditions, was a completely different race so every minute you had to decide something different.
"Why the call came was out of the panic and we have to make up for what we are losing," he added.
Mercedes had won nine of 10 races until Sunday, when Australian Daniel Ricciardo took his second victory of the year for champions Red Bull.
Hamilton was told over the team radio, after his second and final stop with a third of the race to go, not to hold up Rosberg behind him because the German needed to get past to make his three-stop strategy work.
Hamilton made clear Rosberg needed to be a lot closer to overtake and would not slow down or move aside. After eight laps behind him, Rosberg pitted and then had to fight back in a thrilling chase to the finish between the top four.
Ferrari's Fernando Alonso finished second.
The result allowed Hamilton, who had suffered an engine fire in qualifying, to cut Rosberg's overall lead to 11 points with eight races remaining.
Had he let Rosberg pass, the German might have won for Mercedes and extended his lead but Lauda said Hamilton had to look out for his own interests rather than the team's.
Mercedes motorsport head Toto Wolff recognised after the race that the title battle had entered a new phase.
"We cannot really ask either driver to give up their position or jeopardise their own championship chances for the benefit of the team," he said.
Lauda said it was "completely normal between drivers that they want to be in front of the other. So the reaction of the drivers for me is completely normal.
"I think when everything calms down, there is nothing wrong. It was good racing, this is for me the most important, between the Mercedes guys and the rest."
Lauda said Hamilton's race, with a new chassis and engine and starting behind Kevin Magnussen's McLaren in the pitlane, had in any case been the drive of the day.
"This was for me the outstanding drive. Not only (starting) from the pitlane but he had a brand new car which had to be put together. He never drove this car which is a handicap. And then he had to start in the wet.
"So what Lewis did with this unknown car, not absolutely balanced, to go all the way through and finish third was incredible. Lewis did an outstanding job," he said.
Hamilton and Rosberg, son of 1982 champion Keke, are in a duel of their own for the title and the season so far has seen friction between the two rise and fall with every race.
In Monaco, the pair were barely speaking after Rosberg made an error late in qualifying that secured him pole and brought out warning flags that prevented Hamilton beating his time.
In Bahrain they raced wheel-to-wheel with heated discussions afterwards about some of the defensive moves.
Lauda felt the August break between Hungary and Belgium would restore some calm.
"I have been very happy. Nobody had any problems," he said of managing relations between the drivers. "Now I have to see if there are some but I doubt it because everybody goes on holiday anyway and drivers forget quickly.
"After the holidays they start completely normal again."