"We keep giving teams a start in games and here we gave them two goals and 65 minutes," Beattie said.
"That's the way the game went.
"We had an early chance and were a bit unlucky.
"The conditions were horrendous, I can't make an excuse because it's the same for both sides, they've just handled it better."
It was one-way traffic at Highbury as Parkin fired the home side ahead after just six minutes.
Ball and Antoni Sarcevic had chances to extend Fleetwood's lead before the break as Accrington were limited to throwing long balls at Odejayi, starting as a lone striker having extended his loan spell from Rotherham.
The home side did make it two-nil 13 minutes after the break.
Sarcevic charged in to win the ball down the right, surging into the area he picked out Ball at the back post and he doubled Fleetwood's lead.
A double change for Accrington gave the visitors a revived spirit and they pulled a goal back from nothing with nine minutes remaining.
It was the visitors' first effort on target as a soft free-kick floated over the Fleetwood wall by Josh Windass found Odejayi unmarked and he headed home.
The fightback would not last, though, substitutes Stewart Murdoch and Carr combining to claim the points for Fleetwood - the former on the break, the latter applying a composed finish to bag his first goal for the club deep into injury time.
And Stanley boss Beattie was left to praise burly striker Parkin as Town's prized asset
"In the end I think Jon Parkin was the difference," he said.
"He brings that little bit of quality to any side and his finish was first class."