Murphy scored Stanley’s winner in their 1-0 triumph at Bristol Rovers on Tuesday night to move them up to 17th in League Two.
Having been cast adrift at the bottom after only two points from their opening 10 matches, they have now taken 30 points from their next 17 games – virtually automatic promotion form.
That now puts them only three points off the top half and incredibly only six points behind eighth – although the play-off places are a distant 14 points away.
“I totally believe in the players and the position they’ve got themselves into from the position we were in is nothing short of miraculous,” Beattie said.
“We know where we’ve come from, we were in a very precarious position with plenty of people writing us off and it’s down to the lads’ hard work and the belief in themselves.
“The away form is good, we’ve won five out of the last seven.
“We’ll just keep getting the home games called off and keep playing away all the time!”
The Reds’ home game against Bury at the weekend was postponed but they return to action against Morecambe on Saturday at the Store First Stadium, where they have won only three matches this season.
Murphy netted his eighth goal of the season at Bristol Rovers, with five of them coming in the final five minutes of matches.
The 23-year-old midfielder is one of several Stanley players who are out of contract at the end of the season.
“Peter is a good young player and he has got all the attributes to become a very good young player,” said Beattie, who has appeared on odds lists for the vacant managerial position at Oxford United.
“It’s up to Peter, we’ll give him the platform go out there and express himself and as long as he’s disciplined and he keeps getting in the box then he’s going to get noticed.
“Hopefully we can nurture him into a better player for Accrington Stanley but, if he progresses in the way that he and I hope he will, then I think the club will struggle to hang on to him.”
Goalkeeper Marcus Bettinelli is due to extend his loan with Stanley until the end of the season, but Beattie is uncertain whether there will be any more business before the transfer window closes tomorrow.
“I don’t know,” Beattie said. “We’d obviously like to add a couple to the squad maybe but the finances are quite tight.”