The Welshman was the team's top finisher, crossing the line in 54th place after Zdenek Stybar continued Deceuninck-QuickStep's Spring dominance with yet another win.
Team Sky came into the race on the back of a strong set of one-day results. Owain Doull was second in Kuurne-Brussel-Kuurne, while they had picked up top-ten placings in Milan-San Remo, Bredene Koksijde Classic, and Driedaagse Brugge-De Panne.
On Friday, Rowe looked to be in contention until a main group of favourites began attacking on the Paterberg. He was unable to follow as Stybar, Greg Van Avermaet, Bob Jungles, and others opened up the race.
Ian Stannard, who had attacked earlier in the race, suffered a puncture just at the wrong moment and later crashed, while Team Sky's other protected rider, Gianni Moscon, was unable to make an impression on the race. The Italian is still finding his form after a difficult start to the year that saw him abandon Tirreno-Adriatico and miss several races as a result.
Rowe took to Twitter after the race to express his feelings on the day: "Got my head kicked in today at E3, no excuses. Live and learn, onto the next one Wevelgem," he wrote.
The team's director at the E3 BinckBank Classic, Servais Knaven, later released quotes on the Team Sky website, describing the team's performance.
"Ian got a puncture just before Paterberg, which is a key point in the race. (Filippo) Ganna was able to stop and help him change but then he crashed on the Oude Kwaremont which blocked the road. He's okay but he didn't have any luck today," Knaven said.