Glamorgan remain winless in this year's Vitality Blast after losing to Somerset by 25 runs in Taunton.
Chasing 178 to win, only David Lloyd (63) and Andrew Salter (39*) provided resistance as Glamorgan fell to 152 all out.
"We lost a couple of games to begin with and then things became difficult," said captain Colin Ingram.
"Some of our batsmen have struggled and our poor run has stemmed from there. David Lloyd has done pretty well throughout, but the rest of us failed to give him the support he deserved in this game.
"It's hard when you lose several games in a row, but we have a couple left and will look to keep going and bounce back.
The Welsh county handed a T20 debut to seam bowler Roman Walker who impressed with figures of 2/30, while batsman Callum Taylor made his debut for the club.
"We've introduced some younger players to the side to give them experience and they have done quite well. It's a steep learning curve for them though and T20 can be an unforgiving environment."