The Scarlets lifted the trophy for the 12th and last time before regionalisation changes the face of the competition and Welsh rugby.
Jenkins said: "It's the end chapter of what has been an amazing spectacle for Welsh rugby through the years. This competition has played a big part in Llanelli's rugby tradition and so to close that with a win at the Millennium Stadium is fantastic.
"We always knew Newport would bring a big physical presence and attitude up front and that is exactly what they did.
"They competed at the lineouts, the scrums and the tackle area and the result of that was a very close and difficult 60 minutes.
"But in fairness to our players, we stuck at it and wore them down before playing some great rugby in the last 15 minutes to create the result.
"I firmly believe that with the right players, substitutions can have a big impact on a game and that happened with Luke Gross, Martyn Madden and Salesi Finau. All three came on and made a huge contribution in turning the game around."
Meanwhile Newport captain Simon Raiwalui praised his side's efforts for holding the cup kings to within a point up until 13 minutes from time.
"As a captain all I can ask of my players is that they give 110 per cent and that is what every single one did," he said.
"Obviously it hurts to lose but we know we gave everything and made it a real contest but in the end we were simply beaten by a better team."
Llanelli: B Davies (S Finau, 61); M Jones, M Watkins, L Davies (capt), G Evans; S Jones, G Easterby (D Peel, 80); I Thomas, R McBryde, J Davies (M Madden, 61), C Wyatt (L Gross, 52), V Cooper (Boobyer 57, Wyatt, 58), D Hodges, S Quinnell, S Easterby.
Newport: P Montgomery; M Mostyn (O Tonu'u, 83), J Jones-Hughes (N Brew, 67), J Pritchard, A Cadwallader; S Howarth (J Strange, 72), O Tonu'u (D Llewellyn, 82); R Snow, P Young (J Richards, 43-45), C Anthony (A Garvey, 63), S Raiwalui (capt), M Voyle (M Veater, 69), I Gough, S Ojomoh (R Jones, 85), J Forster.