Plymouth counterpart John Sheridan said his side's dropped points could prove costly come the end of the season.
The Pilgrims were on course for all three points after top scorer Reuben Reid had fired home his 19th goal of the season in the 32nd minute.
Victory would have boosted Argyle's play-off chances, but instead they dropped to eighth after Aldred headed home an 81st-minute equaliser.
Beattie believes his side will need around 52 points to stay up and they are currently on 45.
"It's another point towards our target - although we might need more than 52 points," said Beattie.
"All we can do is keep trying to win games and see where it takes us.
"We are playing well, the lads are enjoying their football, but they know when to work hard and they have put a superb shift in.
"It was a brilliant performance in tricky conditions due to the weather, but we are now unbeaten in five at home and we have got to carry this on."
The game was in doubt before kick-off due to persistent rain and the pitch was a quagmire.
Plymouth started well with the prolific Reid denied by the legs of home goalkeeper Marcus Bettinelli before he opened the scoring.
The striker received the ball on the left side of the penalty area and drilled it low and hard into the bottom corner.
The game was end-to-end with both side's creating chances and Accrington substitiute Kayode Odejayi should have done better but he headed over the crossbar when unmarked.
Neal Trotman also failed to find the target in a decent position for the visitors before Aldred levelled when he powered home Lee Molyneux's right-wing cross nine minutes from time.
- Sports & Recreation
- Reuben Reid