Barrow and Couch, who together won the 10m synchro title at last year's Europeans, placed fourth and fifth respectively as the event got underway in Germany.
Competing for the first time in the individual event since 2010, Barrow was second after her first dive but was to eventually finish just 3.75 points off the podium in fourth.
Couch meanwhile started the opposite to Barrow but fought her way back from eighth place to finish with a points total of 300.10 in Rostock.
Oliver Dingley was also in individual, as well as team action with Rebecca Gallantree, on the opening day placing sixth overall in the men's 1m springboard.
Together in the team seven Dingley and Gallantree finished seventh with a score of 327.35 with Ukraine claiming the three gold medals on offer on day one.
Illya Kvasha won the men's 1m springboard and Iuliia Prokopchuk the women's 10m platform before the latter joined forces with Oleksandr Bondar for success in the team event.