Daryl Horgan notched a clinical brace to cancel out Peter Haring’s opener and send Hibs two points clear of the Jambos, having been 11 adrift of their city rivals when Heckingbottom succeeded Neil Lennon in mid-February.
With six wins and two draws from his eight Premiership matches in charge, the Englishman is setting lofty goals as his side approach the post-split fixtures full of momentum.
Heckingbottom said: “Is Europe a goal? Yes. But whether we get there or not, we’ll see.
“We still have to play the teams around us and we’ll need results to go our way and continue this type of form to get there - but we’ll try.
“The problem is that we have handicapped ourselves so much so it’s still a long way away.
“When I arrived, I would have snapped your hand off to just say we got top six assured with a game left. It is a credit to the hard work and performances of the players that we are in the position that we are.
“Now we have the teams around us in the next five games - let’s see where we end up.”
Hailing match-winner Horgan, he added: “He’ll get the plaudits today but looking back over his performances regardless he has been performing really well.”
Meanwhile, Hearts manager Craig Levein was left to rue his side’s profligacy as they slipped to a first defeat to Hibs in Gorgie since May 2013.
Olly Lee struck the woodwork and fired narrowly wide of the post in the first period, while Arnaud Djoum missed a golden opportunity and Jake Mulraney was denied by the legs of Ofir Marciano.
Levein said: “I was pleased with the performance overall. We just didn’t score the opportunities to put the game to bed.
“We have played a hell of a lot worse in recent derby matches and won. There was an inability to be clinical in the penalty box and it has ultimately cost us the game.”
The full-time whistle was met by widespread jeers and even some seething supporters demanding Levein step down.
He added: “When we lose a derby match nobody hurts more than I do. I understand the nature of it and the players understand the nature of it as well.
“There isn’t anyone in the Hearts dressing room who doesn’t feel the same anger and frustration that supporters feel.”
A thoroughly entertaining contest was marred by pyrotechnics being thrown on to the pitch on three occasions - from both sets of supporters - and, remarkably, a coconut appeared to be lobbed from the away section.
“It is a nonsense,” blasted Levein. “It is the first time I have ever heard of a coconut being thrown on.
“Who has got a spare coconut to throw on? Honestly, it is mental.”
Heckingbottom added: “We don’t want things like that happening.”