Shamrock had its chances against the Lithuanian league leader, the best of which saw O'Donnell burst through late only to fire straight at visiting goalkeeper Emilljus Zubas.
Hopes were high after last season's heroics when Shamrock became the first Irish team to reach the UEFA Europa League group stages, but it must now get a result in
Welsh side The New Saints put up a brave performance to hold Sweden champion Helsingborgs to a goalless draw in its first-leg clash in Oswestry.
UEFA Champions League
Borussia Dortmund coach Jurgen Klopp started to believe that his side could win the UEFA Champions League after its dramatic comeback against Malaga.