The Lanarkshire outfit have managed just one victory in the Ladbrokes Premiership this season but have come close to maximum points on five other occasions before settling for draws.
That cruel luck has left the Accies languishing just two points above last-placed Dundee, and Canning accepts his team will have to sharpen up in front of goal if they want to move up the standings.
He said: “I’d say we are in a false position based on how we have played in games and the opportunities we have created.
“That’s just the way it is though. I’m pretty sure if you were to ask the other sides down the bottom they will say the same thing. Kilmarnock played well but lost a late equaliser at the weekend, so did Partick.
“The league is just so tight that one moment in a game seems to swing things.
“The three points are so crucial, so we need to start turning the draws into wins.
“I’m not worried about a lack of goals because we have scored in every league game so far. But while we’ve taken one chance, we’ve not gone on and taken a second or a third sometimes.
“We’ve definitely not scored the number we should have with the chances we’ve created. In the last two away games against Motherwell and Partick Thistle we’ve had 44 attempts at goal but scored just four times. I think that proves there is not a lot wrong - we just need to get ourselves over the line.”
Canning will need to muster all the extra firepower he can when his side host Aberdeen on Tuesday night.
Derek McInnes’ Dons are in jubilant mood after booking their place in next month’s Betfred Cup final against Celtic with their victory over Morton in Saturday’s Hampden semi-final.
“Aberdeen are a top team going forward, with quality all over the park,” Canning said. “Regardless of what happened on Saturday, they would be a threat.
“They have won two games by 4-0 then got themselves into a cup final on Saturday, so they will come here full of belief.
“This is the strongest squad Derek has had since he moved up to Aberdeen. They have match-winners across their front four but they also have depth, with guys who can come off the bench and make a difference.
“But we feel we have guys who can hurt them too. Guys like Ali Crawford have caused teams problems this season. Alex D’Acol is playing well while Eammon Brophy scored last week so hopefully we can come out on top.”