The Jambos boss watched on as his side failed to build on an early lead and ultimately fell to their rivals for the first time at Tynecastle in six years.
Peter Haring had given Hearts the lead with a header in the first half, but Hibs hit back with two goals from Daryl Horgan before then producing a brilliant defensive performance to hold on to their lead.
There were a lot of boos for Levein and his team at the full-time whistle as they lost their third game in the last four and surrendered fifth in the table to their rivals.
But Levein insists the pressure won’t lead to his sacking – and that he’ll be manager of Hearts next season:
It may not seem like Levein and Hearts have struggled of late, producing some big wins against Aberdeen and Partick Thistle lately.
They also face Inverness in the Scottish Cup semi-final at Hampden next week.
But Hearts have really fallen away after starting the season with title-contending form and only have two wins in their last nine league games.