Portugal led 21-0 at the break, although Wales struck back with two tries late on to give Wales respectability.
In the semis Wales beat Georgia 19-14 and beat Belgium 33-12 in their final pool game despite ending with four players after three were sin-binned.
In the semi-final Andy Powell struck after the break against Georgia while top seeds Portugal beat Ireland 14-12 in their semi-final.
London Welsh's Alec Jenkins was first to be sin-binned against Belgium, but while down to four players Powell again scored a try.
On day one Wales beat Poland (38-7), Ireland (26-14), Ukraine (21-17) and Italy (33-12), but they ended the tournament with only eight fit players from their squad of 12