The Lions' coach had taken on responsibility for the team along with Academy FA Director Scott Fitzgerald following the sacking of Steve Lomas after the 4-0 Boxing Day defeat at Watford.
He said after today's Sky Bet Championship stalemate: "I was disappointed and sad for Steve because he's a good guy who worked tirelessly to get it right - and we all share a collective responsibility for what happened.
"We only really had 24 hours to prepare for the game and we are delighted with the response we got from the players.
"But as far as taking the job on - that is for someone else.
"Scott and I both love the club and we will do what we can until an appointment is made but there are no second thoughts about taking it on permanently."
Harris added: "I thought the players were fantastic and it was really good to keep a clean sheet because we have been poor away from home recently.
"I think the performance will give the boys confidence because the desire, commitment and team spirit they showed was phenomenal.
"I've no idea when a new appointment will be made but we will carry on in the meantime and try not to let anyone down.
" Whoever takes over will inherit a fantastic bunch of players and it will be up to them to get the best out of them ".
Millwall had more possession during the game and more of the attacking play overall but were sadly lacking in front of goal.
It was Doncaster who came closest to breaking the deadlock when substitute Federico Macheda hit the post five minutes from time.
Rovers boss Paul Dickov said he was disappointed not to win the game rather than being relieved to end a run of four successive defeats.
He said: "It's great to keep a clean sheet but I thought we should have taken all three points.
"Apart from hitting the post we were through twice on goal and had players pulled back - which was missed by the officials.
"Two big decisions have gone against us and it's very disappointing because it wasn't as if the officials were in bad positions to see what happened.
"It was a scrappy game but the response from the players after the Boxing Day defeat against Ipswich was excellent.
"We had a good chat after that and we said the only way to put things right was to stick together - and I thought we did that today.
"There were three teenagers in the side and I thought they all did really well.
"Young Alex Peterson was asked to play up front on his own and the kid did fantastically well. He's a local lad full of enthusiasm and I'll never be afraid to throw in youngsters like that because you know they'll give everything they've got."
He added: "We'll be hoping to do some business during the transfer window next month . We want to tie up Richie Wellens and strengthen both attack and defence."