Mixu Paatelainen's team could clinch the final place in the top half of the Scottish Premier League without kicking a ball if nearest challengers Motherwell are defeated by St Mirren on Saturday afternoon.
However, with only a single-point advantage over the Fir Park men, the Edinburgh outfit have prepared all week to face Rangers at Easter Road on Sunday knowing they could need all three points to reach their target.
Thicot believes they could go on to claw back the six-point gap to Aberdeen and Dundee United above them should they make it into the top six.
However, he has confessed the praise being heaped on capital foes Hearts following their charge to third place makes their own struggles hard to take.
He said: "We are proud and for the fans and for everybody, especially for us players first, we want to finish in the top six and play against Hearts.
"We want to try and move up the league after that as well, why not?
"It annoys me a bit that Hearts are being praised and getting a lot of attention because I hate finishing second.
"We can't push for the title or for second place but if we can finish in the top six on Sunday then you never know what can happen after that if we win a lot of games in the top six."