Mr Jones and scores of his young charges have been supporting the Welsh warbler - a former pupil - in his campaign to clinch a pound;1 million recording contract.
But the bookies' favourite lost out in a Wales-versus-Scotland final to underdog Leon Jackson by just a few thousand votes.
TV watchdog Ofcom has since launched an investigation after receiving thousands of complaints from viewers who say they were unable to lodge a vote.
Mr Jones said he managed to get through to phone lines after three attempts but added: "Some pupils said the lines were constantly engaged. Rhydian was definitely the best singer there."
Staff at the Welsh-medium primary put up posters around the school urging all pupils to vote. They all passed on good luck cards to Rhydian's mum Angela Roberts and are now sending a special "well done" card in consolation.
Welsh-speaker Rhydian, who prides himself on his operatic voice, represented the 130-pupil school at the Urdd Eisteddfod aged five. He then went on to Llandovery College.
Phil Davies, head of rugby at the college, said: "He was so good he could have played for the Gwent Dragons or Llanelli Scarlets."
Bosses from the ITV1 show's production company Talkback Thames have insisted nothing was rigged. They suggest the sheer volume of calls was to blame.