An injury-time goal from Peter Murphy gave Stanley a league double over Rovers for the second successive season.
After the 1-0 win at the Memorial Stadium a delighted Beattie said: "The lads are starting to believe in themselves as much as I believe in them. I couldn't be more proud of my team.
"It wasn't the prettiest of games, it was never going to be in the conditions. But we stuck at it and to score so late on was a great feeling.
"Peter Murphy is a very promising young player who can become a very valuable one for our club. If he develops as I think he can we will find it hard to hold onto him.
"But all the players deserve credit. To be where we are now from the position we were in is a tremendous effort and we are putting together some decent away form."
A forgettable game was deep into stoppage time and the official figure of 34 travelling Stanley fans made their voices heard.
The home side only had themselves to blame for some sloppy finishing. Kaid Mohamed hit the outside of a post with a 57th-minute shot.
A disjointed first half saw Matt Harrold head narrowly over for Rovers after 12 minutes, while Accrington's Piero Mingoia forced a save from Mildenhall with a low drive.
The best effort of the first half came from Mohamed. The loan signing from Port Vale produced a strong run and fierce shot shortly before the break but visiting keeper Marcus Bettinelli parried the effort.
Rovers boss John Ward said: "We probably played better than we did when beating Newport on Saturday, but couldn't come up with the end product.
"Some of our shots were snatched at, but I was happy with our football up to the opposing penalty area.
"We didn't take our chances and paid the price. But we are a young team and we will pick the players up to go again.
"The next game is a tough trip to Chesterfield and we have to ensure spirits are lifted ahead of that one."
- Sports & Recreation
- Peter Murphy