The Seagulls went into the game red-hot favourites to secure all three points, but were lucky to escape with one after being second-best for large spells.
Indeed, the Lions would have emerged victorious had goalkeeper David Forde not allowed Kazenga LuaLua's 88th-minute free-kick to squirm through his grasp.
"It's just one bad day at the office, too many mistakes but a great point for us," Poyet told The Argus.
"I know it sounds bad but it's not and credit to Millwall, because I like the way they play.
"It was always going to be a difficult game because I have been watching Millwall and people are not giving them the credit they deserve.
"Their recruitment in January was excellent. They have got players who can pass the ball."