Paulo Sergio says it would be unrealistic for his side to push Rangers for second place in the Scottish Premier League.
The Edinburgh club face Motherwell on Saturday, knowing a victory would take them within three points of the team in third.
Rangers then would be at most 12 points ahead of Sergio’s men, with 11 SPL games left to play, with the Ibrox club have been docked ten points for going into administration.
The manager though believes finishing in their current position would mark an achievement for his team, having endured their own financial troubles this campaign.
"We have fought our problems and did what we have to do, nobody can ask for Hearts to be second or third place this season after what has gone on this season," said Sergio.
"I think if we achieve third or fourth place this season, it will have been a great result after a hard season.
"During the transfer window we lost three big players in Ryan Stevenson, John Sutton and Eggert Jonsson, so it has been difficult.
"We recognise the good job that Stuart McCall is doing at Motherwell, they are a very strong side with good organisation, but I believe we can beat them on Saturday."
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