The French club made it two wins from two in the competition on Sunday when they saw off Cardiff Blues 22-14 at Cardiff Arms Park.
"Cardiff is a tough place to come and get a result and we knew we had to grind it out to show people we can win the tight games," said Armitage.
"Every win now helps towards a possible home quarter-final. We want to be a top contender in this tournament and that means we have to win every game to get that home advantage."
Toulon continue their European campaign on December 8 when they face Sale Sharks at the Salford City Stadium.