And the Partick Thistle star is determined the Jags won't be dragged into the scrap for survival as they bid to end their recent poor run of form against Hibernian today.
Alan Archibald's side have a 16-point advantage over the Jambos after they were hit with a hefty deduction at the start of the season for going into administration.
Thistle have struggled in recent weeks but midfielder Osbourne is only looking onwards and upwards.
He said: "I am just thinking about us. At the moment, Hearts don't seem to be gaining on anyone.
"We have just got to think about our own performance and not Hearts.
"If they ever do catch us, we deserve to go down considering how many points they were away from us.
"We are just concentrating on our own performances.
"Hearts are a massive club, they have got a great fan-base. But they had so many points deducted and their squad is so young.
"If they were to do it, it would be a great achievement. But you have got to look at yourself.
"If you get caught by a team that many points behind you then you haven't won enough. We are out there concentrating on our own game every week.
"We are not thinking about anyone else. We have got to make sure we stay in this league."
Thistle head to Easter Road this afternoon having recorded just one win in their last 11 Premiership fixtures.
They have slipped to ninth in the standings after an impressive start to the campaign and Osbourne admits it is hard to haul themselves out of a sticky patch.
He said: "You have got to just keep working hard. Sometimes when you are going through a slump it is hard to get out of it.
"When we do get our next win, hopefully we can go on a run."
While a lack of goals has plagued Archibald's side for most of the campaign, their defensive frailties have been badly exposed in recent weeks.
The Jags have shipped 12 goals in their last four outings and Osbourne knows they must shape up at the back as they gear up for their capital clash this afternoon.
He said: "As a defensive- minded player myself, I don't think it has been good enough.
"If people want to criticise, they can criticise."