Robbie Neilson has been urged to start picking up results against Celtic and Rangers for the sake of Scottish football.
Hearts are currently clear in third position, but during Neilson's tenure as boss, the Edinburgh club have struggled to defeat either side of Glasgow's big two.
Fans are becoming frustrated in Gorgie and former player Ryan Stevenson insists the Jambos have to improve when taking on the top talents in the league.
Following Saturday's Scottish Cup defeat to Celtic, he told the Daily Record: "It was just too easy in the end. The Joe Hart save was a big moment but the second half was a non event. If they had gone hell for leather for an hour and then got picked off, I think I would have accepted it more.
"By the end it was just a bit dispiriting though. We know Celtic are light years ahead right now and Rangers are strong as well. But Robbie Neilson could really do with getting a result against them from time to time.
"Of course it’s easier said than done but that is the demand of the job. The fans don’t expect to be beating the Old Firm all the time. They do demand their team at least makes life difficult for them when they come to Gorgie and they give them the odd bloody nose.
"From the outside it feels like the season is petering out but there is still a huge amount to play for. A lot of people will be taking about the gap but it doesn’t matter if Hearts finish four, 14 or 40 points behind the Old Firm – all that matters now is they finish third.
"That is likely to secure European football to Christmas next season and give them the cash that might help them do better the next time the Glasgow clubs come calling."
Hearts were missing forwards Lawrence Shankland, Stephen Humphrys and Yutaro Oda as well as key midfielder Robert Snodgrass at the weekend and a number of long-term absentees.
“There’s nothing you can do about that,” manager Robbie Neilson said. “It creates opportunities for guys to come in and I thought Josh Ginnelly led the line well.
“Barrie McKay did well for us in those wee areas – we asked him to do a bit of a different role on Callum McGregor.
“Other guys coming in, I couldn’t ask any more in terms of work-rate. At times, the decision-making and quality wasn’t there.”
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