Accies had gone 13 games without victory since their last success on January 4, but goals from Jason Scotland and Ali Crawford ensured the team won the last Lanarkshire derby of the campaign.
“It’s a great night and a good result,” Canning told a BBC Radio.
“Tonight the boys got exactly what they deserved. They were all over Motherwell from start to finish.
“We played really well, we controlled the game. We played with professionalism and an experience that I enjoyed watching.
“It’s been tough. From a personal point of view I haven’t been too concerned, the club have been great.
“It’s more for the players to give them the belief that they’re still the same players that did so well at the start of the season.
“In my nature I want to win. Obviously I wanted that win as soon as I could get it. Tonight wasn’t about me getting a win, it was about the players getting what they deserved.”
Motherwell counterpart Ian Baraclough rued his side profligacy at New Douglas Park on a night when their chances of catching the pack of teams above them suffered a major blow.
The Steelmen could drop nine points behind third-bottom Ross County should they win on Saturday, and with four more games remaining would be almost certain to play Championship opponents in the play-offs to secure Scottish Premiership football next season.
Baraclough said: “I’m frustrated that we have created more chances and better chances, and to come away without scoring is amazing for me. We just weren’t clinical enough.
“We created good chances, there were six or seven at least that I counted, we hit the woodwork a couple of times and their keeper has pulled off a couple of good saves from one-on-ones. That has cost us.
“Their two goals have come from positions of good possession, we have given it away cheaply, they have broken and been clinical. There’s the difference.
“We still have to believe we can bridge the gap.”