But the Wales wing says the Scarlets only had themselves to blame for not ensuring victory.
He said: "To get so close to a victory - we only have ourselves to blame there.
"We had the opportunity to put the ball dead there [at the end] and it didn't quite happen for us.
"The best sides punish you when it comes down to the little things and those are the little things we need to get right and unfortunately we're losing out, sadly, at the moment.
"We made a huge stride forward and we felt as a squad we were a lot better than we showed last week [in defeat at Glasgow].
"We're in the game and in the business of winning things and unfortunately at the moment we're falling the wrong side of the line.
"It won't stop us coming back here and working hard next week to try and get a vital victory in another Welsh derby.
"We can take a lot from the game, but we're bitterly disappointed and we needed a victory there, but there you are."
Jones says he is looking forward to the rest of the season after some outstanding performances, including from official man-of-the-match hooker Ken Owens.
Jones said: "It's early in the season and there were some fantastic performances - from Ken [Owens] and many others - and I'm looking forward to working with these guys for the rest of the season.
"I'm sure there'll be many good victories to come here at Parc y Scarlets."
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