That defeat extended the Dragons' winless runs to eight games, while they have only won two of their last 14 matches.
Wales face Scotland at Murrayfield in their second game of the Championship with the Kiwi under increasing pressure to turn around their nightmare run of results.
But WRU chief executive Roger Lewis has come out in support of Gatland, stressing he will continue at the reins regardless of the current campaign and lead Wales into the World Cup.
"This is a time for cool heads and certainly not to chop heads," said Lewis.
"At the top of the WRU we believe we have the right people in place with the right skills and experiences."
Gatland led the men in red to the Grand Slam in 2008 and was given a four-year contract extension in October.
"Our coaching team know what is required to win Grand Slams and European Cups as well as how to face defeat," he told the Daily Telegraph.
"To gain respect we first need self-respect and to do that we all need to take responsibility. No-one is making excuses, it is up to all of us in the WRU to front up to this together and move forward."