A hat-trick from Lee Gregory – including two penalties – left the south London outfit with a 3-1 lead going into the final 20 minutes on Saturday, Tom Ince registering for Derby.
But Chris Martin reduced the arrears from the spot, and Jeff Hendrick equalised for the Rams five minutes from time.
Millwall play their final Sky Bet Championship match of the season at Wolves next weekend, but will be relegated on Tuesday should fellow battlers Rotherham win at home to beaten FA Cup semi-finalists Reading.
Harris said: “I can’t pick the players up at the moment. They will come in on Monday morning and pick themselves up, and we have to sit and wait to see how Rotherham go on Tuesday.
“It’s really simple: if Rotherham get the win on Tuesday we’re relegated. I won’t be watching the game.
“At the moment, whatever league we’re in, next year’s squad will be dominant at home. They’ll be young, athletic and hungry, and play with the Millwall spirit.
“The home record this term hasn’t been what it should have been. That’s not through lack of effort, certainly not, but that’s going to be the starting point in the summer.
“The players as a group are built on hope and belief and to come from being on the run they were on and to get the performances and results that they’ve got has been testimony to them as a group.
“I certainly am not accepting perspective and ‘well dones’ for achieving some points, especially at home. The bottom line is if you play for Millwall Football Club you have to win your home games.”
Derby have now won just two of their last 12 games and need a positive result next weekend to ensure they reach the play-offs.
Boss Steve McClaren said: “We’re making hard work of everything. You expect to score three and four away from home and win games.
“We’re not even thinking ahead of next week. We’ve got a job to do and we need to keep character.
“We can score goals to win games – we just need to score more than our opponents.
“I really cannot believe the character of this team – they’re whole-hearted, they’re honest, they go for 95 minutes and they deserved to win. They could easily have got angry and frustrated at the referee’s decisions, but they huddled up after every goal and came back.
“I don’t know what the referee is doing to give those decisions. I haven’t seen them again, but it wasn’t even a handball (for Gregory’s first penalty). He (Derby captain Richard Keogh) is sliding across and I’m not sure it even hits his hand – it hits his thigh.”