Warren Gatland's men ran over six tries in a 51-3 thumping, with Greig Laidlaw's third-minute penalty offering the only resistance for Scotland in Cardiff.
And Hogg, who personally apologised to Biggar after the game, insists his rush of blood does not reflect the type of player he is.
"I would like to apologise to my teammates, the Scotland management and all Scotland supporters for what happened. I have let people down," said Hogg in a statement released by the Scottish Rugby Union.
"I have said sorry in person to Dan Biggar and I have apologised to the referee, Jerome Garces.
"I always try to play hard and fair and what happened was out of character for me. Once again, I'm very sorry."