The 22-year-old, who started all five games and scored three tries in Wales' RBS 6 Nations Grand Slam triumph earlier this year, helped his side to a 16-8 lead alongside Welsh colleague Leigh Halfpenny who kicked 14 points.
But a late penalty try and conversion, followed by a drop goal from Greig Laidlaw sealed a dramatic comeback to break the Blues' hearts as they failed to make it a fairytale return to their former ground after three seasons at the Cardiff City Stadium.
And Cuthbert was adamant that his own performance didn't matter a jot because of the final scoreline.
"It's frustrating to lose the first home game because we wanted to make the Arms Park a bit of a fortress and go unbeaten," said Cuthbert, whose fellow winger Tom James also impressed.
"Defence was one of my weaknesses at the start of last season and I have worked hard with the Welsh squad last year and pre-season with the Blues on it.
"Phil (Davies) is really good on things like that and I am just glad it is hopefully coming together.
"Fair play to Tom James, he made those breaks himself really and he did well to get there. It's a shame we didn't execute one. If we had executed one we might have won the game.
"It's a shame we lost by three points but we have got to take the positives I guess and work on them for next week really."
Elsewhere, Wales star George North took his tally for the season to three tries in two games as the Scarlets inflicted an 18-13 defeat on Glasgow Warriors in their new home at Scotstoun.
Aaron Shingler's try gave the Scarlets a 5-3 lead against the run of play before Andy Fenby touched down in the corner.
North, who became the youngest player ever at 19 to reach ten international tries with his opener in the RBS 6 Nations win against Ireland in February, added to his double against Heineken Cup champions Leinster last week by crossing again.
Connacht fly-half Miah Nikora did for Zebre on their RaboDirect PRO12 home debut by kicking 15 points in a 30-17 victory in Parma.
Connacht put defeat to the Blues behind them with tries from Mike McCarthy, George Naoupu and Tiernan O'Halloran while Samuele Pace and Dries van Schalkwyk touched down for the Italian side.
And Doug Howlett's try helped Munster make it two wins from two as they saw off Treviso 19-6 at Thomond Park.
Treviso had shocked reigning champions Ospreys 12-6 on the opening weekend but Howlett and 14 points from the boot of Ian Keatley ensured they could not repeat their heroics, with Alberto Di Bernardo's two penalties not enough for the visitors.