New Hearts head coach Wouter Vrancken bemoaned the set-piece blows in Austria that left his side with a mountain to climb to keep their Champions League hopes alive.
The William Hill Premiership runners-up lost 4-0 against Sturm Graz in the first leg of their second qualifying round tie.
The Jambos conceded simple goals from a long throw and a corner early in each half and gave up a further two amid some poor defending before the hour mark.
Landry Kabore and Alexandros Kyziridis squandered excellent first-half opportunities for the visitors and they failed to work the home goalkeeper from about half a dozen reasonable chances in the final half-hour.
After a hugely disappointing debut, Vrancken told Hearts TV: “For me we were killed by two set-plays and this is very difficult to accept, because we started okay.
“We got the first goal against, then we got control of the game and created some chances. We were not efficient and they were.
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“I was pleased with a lot of things that I saw in the game. We could do better. We could have taken more responsibility to have the ball instead of just watching and reacting.
“But it was a pretty good first half, the only thing that was missing was goals.
“We kept believing at half-time but we missed a big chance and then again a set-piece.”
Hearts now look highly likely to drop into the Europa League, where they would face Benfica or St Gallen.
Defeat in that encounter would leave them needing to win a Conference League play-off to achieve league phase football.
Vrancken warned: “Efficiency is very important at this level. When you don’t kill, you get killed.”
