The Dragons are 11 points off the play-offs with two games in hand, meaning they could cut the gap to five by winning those games.
"We've got the bit between our teeth now and are going in the right direction," said Saunders.
"If we win the next three games in front of us we're back in the promotion race."
Saunders has been buoyed by the arrival of striker Andy Mangan from Forest Green in the January transfer window.
Mangan has scored two goals in his first two games, including the winner against Mansfield.
"I knew if we could get a goal scorer we'd shoot up the league," Saunders added.
"We've conceded very few goals. We're just not taking the chances."
Saunders also praised debutant winger Luke Holden who came off with four minutes to go.
"Luke's a good character, he talks a lot, and has got a bit of aggression. He put some great crosses in," he said.
"He was feeling his hamstring at the end - I hope it was cramp."
And Holden himself is hoping to be in shape for the trip to Eastbourne on Saturday and help the side push on.
"I'm very happy with my debut, I was just missing a goal," said the former Liverpool youngster.
"It felt like I hadn't played for weeks, my legs were just a bit tired. I'm just hoping to recover for Saturday to be able to push on.
"The lads are all made up, we've taken 10 points in 10 days and it's not often you do that.
"The lads are all ambitious, we know that if we play well we can beat anyone. Games can't come quickly enough at the moment."
Wrexham will be without midfielder Christian Smith for the next two games after being sent off in injury time.
Source: BBC Sport
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