Plant-based products in fish diets are valuable protein alternatives to fishmeal for the aquafeed industry. Many plant feed ingredients contain polyphenolic compounds, including tannins, which can have beneficial or adverse effects. The tolerable threshold of ingested tannins is unknown for marine carnivorous fishes. We studied the effects of tannic acid (TA) supplementation to the diet of juvenile European seabass (Dicentrarchus labrax) by measuring growth, feed utilization and digestibility, and carcass composition. We randomly allocated groups of fish (initial mean body weight of 10.2 ± 0.7 g; n = 40 fish per tank) to 12 replicate cylindrical-conical tanks (three per treatment). The fish were assigned to one of four dietary treatments for five weeks: control diet (C) with tannin-free protein sources (mostly fishmeal as the base diet, containing 55.7% dry matter (DM) crude protein, gross energy 22.3 kJ g−1 DM) and three experimental diets supplemented with 10, 20, or 30 g TA kg−1 (called TA1, TA2, and TA3, respectively). Tannin ingestion resulted in significantly decreased cumulative feed intake, growth, feed and protein efficiencies, apparent digestibility coefficients, hepatosomatic index, and carcass lipids. The protein digestibility in fish fed the 10 g kg−1 tannin-containing diet was significantly lower than that in fish fed the control diet. This threshold should be taken into account when using novel terrestrial and aquatic plant ingredients for temperate marine fishes.