The U's were the better side for long periods of the game at the Keepmoat Stadium but came away empty-handed after David Cotterill scored a stunning match-winner six minutes from time.
The winger capped a mazy run with a curling shot into the roof of the net for his 10th goal of the season - a strike that Saunders believes will now not see his side relegated.
"We've got 50 points now and that means we should be safe and not get relegated," said the Welshman.
"I think the last game against Sheffield United, when they pinched a point after we had been two goals up, took its toll on the players physically and emotionally because we couldn't seem to get going at all.
"But when we don't get it together we have the ability to keep a clean sheet and not give anything away.
"I've got a team that's full of character that knows how to win without playing brilliantly but the goal we scored was worthy of winning any game.
"It was a brilliant finish and the only dilemma I have is whether to play David Cotterill on the left or the right."
Saunders added: "We introduced a couple of new players. Emile Sinclair made his debut and he is only going to get better because he hadn't even trained with us and only met the players a few hours before the game.
"Lee Fowler made his mark after coming on as substitute. He's gone wrong in the past but he's got a Premier League brain - he's a class player and he's settled down now."
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- David Cotterill