A try from debutant winger Lome Fa’atau was countered by Lifeimi Mafi who crossed for the visitors.
After the game, Warriors head coach Sean Lineen said: “The ambition is a lot higher here now so I’m not happy with the draw.
“I thought we had the better of the first half and Munster had the better of the second.
“The level of skill and ability has to rise to our ambition.”