Cowdenbeath boss Jimmy Nicholl admitted a draw was a chance lost to really get among the strugglers in the Championship relegation zone.
The Fifers dominated possession, even against a gale, but conceded the lead twice through indifferent defending.
Striker Greg Stewart’s double ensured the point but Cowdenbeath had so many chances in the second period they should have achieved the three points they were needing.
Cowden are still five points behind Alloa and three behind Raith Rovers in the battle to avoid the relegation play-offs.
A superb performance by Wasps’ goalkeeper Scott Bain did not help the Cowden cause as his side were getting swamped against the wind in the second-half.
Nicholl said: “That was simply a big chance lost to really improve our position.
“We lost two poor goals through Alloa players being given too much space in the vicinity of our penalty area, and to the lads’ credit they fought back superbly and Greg Stewart scored two cracking goals but we should have had a whole lot more.”
Alloa took the lead in six minutes when Graeme Holmes was given too much space after making a run into the Cowdenbeath box, and he finished well.
But in 37 minutes Stewart levelled after a run which took him past three defenders.
Cowden forced five corners in the opening minutes of the second-half and Bain denied Natt Wedderburn, John Armstrong and Stewart. Then in 58 minutes Ryan McCord shot home from 18 yards to restore the Wasps’ lead.
Cowden came back at the visitors with wave after wave of attacks, but Bain continued to defy them. In 72 minutes Stewart levelled with a fine 12-yard left-foot volley.
There was more good work from the Alloa keeper as time ran down, most notably a fine stop from sub Kyle Miller in added time.
Alloa boss Barry Smith praised his side for their work in withstanding the Cowdenbeath onslaught.
“It was a good battling point for us at a place which it is very difficult for teams to leave with anything,” he said.
“However, on the down side we were twice ahead and we should have been able to develop these situations but the team gave everything and Scott Bain made key saves at key times.”