Holloway watched his side go 4-0 down in the first half as high-flying Boro blew away the struggling Lions at The New Den before running out 5-1 winners.
"I apologise to the supporters for that performance," Sky Sports News quotes Holloway as saying after yesterday's game.
"That team was unrecognisable. I won't blame anybody because the responsibility is mine. I'm shocked and horrified.
"It was an awful day, probably my worst in football. But it will make us stronger."
Defeat leaves Millwall 20th in the table, two points above the Championship drop zone.
They are six games without a victory and have won just one game since August.