The play in question occurred with 6:48 left in the first period when Lucic was given a penalty for charging into Miller.
Both players were going for the puck with the collision happening inside a faceoff circle.
Miller played through the second period before being replaced in the third and Buffalo stated that Miller has a concussion and will miss significant time.
Buffalo head coach Lindy Ruff said after the game that he thought it was a major and added further.
"If it's open season on the goalies then let's get at it," said Ruff.
However, NHL vice president of player safety and hockey operations Brendan Shanahan stated that the play was reviewed and that no further punishment to Lucic was required.
"The minor penalty called on the ice was the correct call," said Shanahan. "And, while it's unfortunate that Miller was hurt I saw nothing egregious about this hit that would elevate it to supplemental discipline."