Hrustic combined twice with team-mate Filip Kostic to score in sixth and 22nd minutes for the Bundesliga side, but Strasbourg, which plays in France's Ligue 2, hit back twice before Habib Diallo bagged the winner eight minutes from time.
Frankfurt coach Oliver Glasner fielded a strong line-up in the first half, with the likes of Kevin Trapp, Martin Hinteregger, Tuta and Sebastian Rode all playing their first friendly of the summer.
"The defeat is self-inflicted because of defensive mistakes," Glasner said after the match.
"Apart from that, we gave little away and there were lots of bright spots. Overall it's a nice match to analyse, for example in terms of how we can cover better. Going forward we had good ideas with probing runs, especially in the first half."