Greg Docherty scored the only goal of the game at New Douglas Park to keep the Accies in the division for an unprecedented fourth consecutive season.
Speaking afterwards, Canning, who replaced Alex Neil as boss in January 2015, said that the feat was testament to his players' "appetite" and "team spirit".
"Every season we're tipped to go down and that's the last three we've managed to stay in the league," he told BBC Sport. "It's a record for the club to stay in the league this long.
"The league doesn't lie - so many times we've been in a similar position and haven't been able to see it through and it's ironic that our downfall through the season has been our greatest achievement today, that we kept a clean sheet after going a goal up. You know the first goal is going to be so important.
"The club tries to get players in with the right appetite, that they want to work. You saw the team spirit today. The fans gave us great backing and I'm delighted for them. The budget is important but the majority of our work for next season is done. The club has a model that they stick to. Everybody works so hard. We'll be in tomorrow and we'll get a wee chat. I've told them to enjoy tonight."
The Accies finished 11th place in the table this term, just one point above relegated Inverness Caledonian Thistle.