Stand-in skipper Richard led the player apologies to caretaker manager Paul Warne as an emotional day at Burton Albion ended in defeat.
Club legend Warne, placed in temporary charge after the shock resignation of Kenny Jackett last week, fought back the tears after the 2-1 Championship loss on Saturday.
He revealed that Wood, captain in the injury absence of Lee Frecklington, had made a beeline for him after the final whistle to say how sorry he was.
“I think they really wanted to win,” said the fitness coach. “When I had Woody and a couple of the senior pros apologising to me, it nearly had me howling.”
Warne, a former Millers player, will return to his role as fitness coach when a new manager is appointed by the division’s bottom club.
“If we had won the game, and everybody would have been on a wave of euphoria and optimism, I dont think the rush would have been as much,” he said.
“After defeat, you can see there are problems, and, knowing the chairman, he will want to sort that quickly. I would wholeheartedly agree with him.
“Let’s get someone in, someone better than what we have got, to help us out. I will do it as long as the chairman wants, but I think something will happen sooner rather than later.”
Burton boss Nigel Clough had commiserated with Warne during the match as Rotherham’s run without a win stretched to 15 matches and they slid 13 points from safety.
“Their manager has been a gentleman,” Warne said. “I always imagine the opposition manager to be the enemy but, to be fair, he was speaking to me throughout the game and he said to me with five minutes to go: ‘Warney, you can just tell you haven’t got any luck.’
Jackson Irvine and Matty Palmer put Albion ahead before Tom Adeyemi scored a consolation goal deep into time added on.
“We had a few flashes but we just couldn’t get the ball in,” Warne added. “The lads tried to create a few things, but I just think they are low on confidence.
“When things don’t go well when you’re top of the league, you have that belief you are going to get back into it.
“When things don’t go well in our position, some of the lads might crumble. That is the harsh reality.”