They were disciplined, they were committed, and they played as a team. That they could not claw back four goals against a team of such evident technical ability was no disgrace, and they walked off at the end to a deserved standing ovation from their supporters.
It was a match which had actually been in danger of not going ahead after a test on a back-up generator caused a minor fire in one of the floodlight pylons almost two hours before kick-off. It was only towards seven o'clock that the German referee decided that the game should proceed with three pylons in operation, and his decision was proved correct as there was no problem at all with visibility.
Having already had his selection plans affected by injuries to Eggert Jonsson and Calum Elliot, Laszlo was forced into a late rethink by a hip injury to Lee Wallace. The left-back could have played at a push, but it was decided to save him for Sunday's SPL match at St Johnstone, and Jose Goncalves took over from him. As promised, Craig Thomson came in to make his first senior start on the other side of defence, and Ismael Bouzid partnered Marius Zaliukas at centre-back.
Michael Stewart, like Zaliukas suspended from last Sunday's 2-1 defeat by Rangers, returned to captain the team from central midfield, where he was joined by Ruben Palazuelos. Suso Santana and David Obua were on the flanks, and Gary Glen started up front alongside Christian Nade.
The decision to go with a 4-4-2 formation instead of 4-5-1 was an indication of Hearts' eagerness to play an attacking game no matter how forlorn their position might seem, and they opened brightly with a move down the left. In just the third minute, however, Dinamo showed how dangerous they could be on the brink, cutting Hearts open with two swift passes. The second found Dimitrios Papadopoulos on the right edge of the penalty box, and his low shot across goal was wide of the far post by a matter of inches.
The Croats could afford to miss such chances, but Hearts needed to take advantage of anything that came their way. After little more than a quarter of an hour they did exactly that.
Goalkeeper Tomislav Butina, possibly showing the first sign of complacency from any visiting player, gathered a cross and threw it straight up the middle to Milan Bajelc. A heavy first touch let Stewart in to intercept, and the home captain sped into the box, jinked to the left past one defender and with two more closing in wrongfooted Butina with a left-foot shot into the opposite corner of the net.
Tynecastle erupted, and momentarily the home support allowed themselves to dream of the most improbable of comebacks. The contingent of around 300 Dinamo fans were unperturbed by this minor blow to their team's self-respect, remaining on their feet, chanting continuously.
The glimmer of hope which Stewart's goal had provided almost became significantly brighter a dozen minutes later. A cross by Thomson from the right was headed back across goal by Obua, then headed back to the left by Glen, and Stewart's acrobatic effort from ten yards crashed off the bar and out, taking the slightest of touches from a defender on the way.
Hearts were playing with far greater purpose and organisation than they had shown in the first leg, and Dinamo were some way below their best. Even so, the impression remained of the team from the Croatian capital that if they really needed a goal they would be able to conjure one up in a couple of minutes, and before half-time efforts from Pedro Morales and Badelj reminded Hearts that they could not relax for a minute.
The second half had no sooner started than Zaliukas needed treatment for a head knock. While he was being seen to, some flares were let off by the Croatian fans and appeared to set light to a small number of seats. The second minor fire of the evening was soon extinguished, but stewards and police formed a tighter cordon round those supporters.
Hearts had come out early after the break, eager to get back into action. They knew they needed a second goal relatively quickly, and they got it within ten minutes at the end of a sustained period of attack. A corner by Thomson from the left was headed out, but then miskicked by Sammir only as far as Zaliukas. The big Lithuanian kept his shot low and straight and found the goal from around 18 yards out.
Laszlo brought on first Gordon Smith then Andy Driver in a bid to keep the tempo up. It was asking a lot of both players: Smith, an 18-year-old striker signed from Livingston, was making his debut, and Driver was playing for the first time since being injured towards the end of last season. The England Under-21 player was also playing through the middle with Smith instead of in his usual position on the wing, but he was soon testing the pace of the Zagreb defence with the ball at his feet.
Dinamo were also asking far more questions of the Hearts defence than they had done in the first half. Papadopoulous came closest with a fierce drive, but Balogh was equal to the challenge and punched clear.
Having been pinned back in their own half for a time, Hearts came off the ropes in the last quarter-hour. With eight minutes to play Obua had a good chance to set up a dramatic finale, but his volley on the turn went over the bar.