One of their clubs will be consigned to automatic relegation after Saturday's final Scottish Premiership fixtures, with Accies presently ahead by a point.
Manager Canning said "it means everything to everybody" at his club.
But he said: "Richie's saying what I would expect him to say, but the pressure is still on Inverness."
Caley Thistle's 2-0 win over Dundee on Wednesday - their second victory in three games - has resurrected their hopes of avoiding automatic relegation as they prepare to host Motherwell.
Accies have, meanwhile, lost four games in a row and presently occupy 11th spot, which comes with it a play-off against the winners of Friday's semi-final between Championship clubs Falkirk and Dundee United for a top flight berth.
"I said a long while ago it would probably come to the last game," said Canning, whose side entertain Dundee. "But I didn't think it would be only ourselves and Inverness involved in it.
"He (Foran) is trying to take all the pressure off his team and on to our team, which is a natural thing to do.
"But, trust me, there's still a load of pressure on Inverness because they have still got to win their game and if we win our game and take care of our job then it doesn't matter what they do.
"For the first time, they've got an opportunity to catch us, but they have got to go and win their game still."
The frustration for Canning is missed opportunities in recent matches, including Tuesday's 3-2 defeat away to Ross County which the hosts won courtesy of Jonathan Franks' stoppage-time goal.
"The Ross County game was the worst I've ever been involved in in terms of getting a feeling that every break is going against you," said the Accies boss.
"We played really well and had a lot of opportunities and didn't get one break. Hopefully they come on Saturday.
"The last couple of games have been tough on us.
"If we can replicate that performance from the other night then hopefully that's enough to get the three points."
Canning retains belief in his players' ability to avoid relegation.
"It has been in our hands and we have lost four games in a row, which isn't acceptable at this stage of the season, and that's going to put you in trouble," he added.
"For us, yes, there is pressure, but it is no more so than it was on Saturday and on Tuesday.
"We need to make sure we go and win and, if we get three points, it doesn't matter what Inverness do."

Ceredigion council unanimously voted to impose the ban following concerns over the impact on land, wildlife and farm life.
The move was proposed by councillor Mark Strong and seconded by councillor Catrin Miles.
In October 2013, the Welsh government called on councils to make a stand, stopping short of an outright ban.
Martin Canning has dismissed as mind games Inverness counterpart Richie Foran's suggestion that the relegation pressure is on Hamilton Academical.
[NEXT_CONCEPT]
Releasing Chinese and air lanterns on council land and beaches in Ceredigion has been banned.