Referee Stephane Auger assessed Burrows separate penalties for diving, interference and unsportsmanlike conduct during the third period of Vancouver's 3-2 loss to the Nashville Predators on Monday.
Burrows later touched off a league-wide controversy by saying Auger told him during the pre-game warm-up that he was "going to get back at him" for making the referee look bad in a previous game.
Auger had assessed a major penalty and game misconduct against Nashville's Jerred Smithson for a hit on Burrows on December 8. However, the league later overturned that misconduct penalty against Smithson.
"The ref came over to me and said I made him look bad in Nashville on the Smithson hit. He said he was going to get me back tonight and he did his job in the third ... ," according to a quote in the NHL's statement that was attributed to Burrows.
The NHL said it conducted an investigation and could not substantiate Burrows' account of Auger's comments.
"The National Hockey League will not tolerate the personal nature of the comments Mr. Burrows directed at referee Auger or the fact that he brought into question the integrity of both the official and the game," Colin Campbell, the NHL's senior executive vice president of hockey operations, said in the statement.
"We have determined that Mr. Burrows' account of referee Auger's comments to him before the game, and specifically Burrows' suggestion that these comments indicated bias against the player or the Vancouver team, cannot be substantiated."
Burrows' comments sparked widespread debate over whether officials hold grudges against certain players and teams.
It has long been believed in hockey circles that players have been reluctant to criticize officiating for fear of reprisals.
(Writing by Steve Keating; editing by Frank Pingue and Peter Rutherford)