It was the Saints first away defeat in Europe in three years, Tommy Wright’s team have emerged unscathed from trips to Rosenborg, Minsk, Lucerne and Spartak Trnava over the past two seasons.
But they were undone at the Vazgen Sargsyan Republican Stadium in Yerevan as Mihran Manasyan’s second-half winner gave the Armenians a narrow lead ahead of the return leg.
Saints substitute Chris Kane did have a chance to level at the death but fired straight at home keeper Gevorg Kasparov to leave the Scots frustrated.
With new signings Joe Shaughnessy, Brad McKay and John Sutton in their line-up, Saints played into the hands of their hosts with a string of sloppy passes.
Midfielder Murray Davidson was forced off for treatment to a head knock inside the opening 90 seconds after colliding with keeper Alan Mannus.
Davidson returned after six minutes on the sidelines but St Johnstone were happy to see Alashkert do little with the time and space they were being given.
Conceding a goal sparked the Saints’ attack but Alashkert were composed in defence and creative in their counter-attack, holding on to the one-goal lead.
This is the fourth consecutive season St Johnstone have played European football and they are pushing to reach the group phase of the competition for the first time.
Saints will now prepare to overcome the one-goal deficit at the return leg at McDiarmid Park on July 7.