Coach Nigel Davies says the Scarlets lack the mental strength needed to win tight games.
Saturday's 13-6 home loss to Magners League leaders Munster means the Scarlets are now unlikely to qualify for the end of season play-offs.
The Dragons are also closing on the Scarlets to claim the third Heinken Cup spot available to the four Welsh teams.
"At times we play some good stuff but we just haven't got that winning mentality at the moment," Davies said.
"It's obviously been frustrating in terms of a few of the results. Performance-wise I think we're certainly going in the right direction and there's a lot to be optimistic about with this group of players."
The Scarlets had matched Munster blow for blow at Parc y Scarlets and the game was poised 6-6 deep in the final quarter.
But when a Welsh attack broke down on the halfway line, Munster wing Simon Zebo fly-hacked the loose ball downfield to score the deciding try.
"The first half we missed some golden opportunities and we could have taken control of the game," Davies added.
"In fairness to Munster they defended very well, they were very good at the contact area which caused us a lot of problems.
"I asked the boys to cross the line in terms of getting that winning mentality and we... failed to do it.
"That's the next step for this team unfortunately, that we can put performances in but at key moments we become inaccurate and we lose compsure, and because of that we're losing games."
The Dragons' 32-28 win over the Ospreys on Friday night saw the Rodney Parade side close to within eight points of the Scarlets, with a game in hand.
With Cardiff Blues four points ahead of the Scarlets, and having played a game less, and the Ospreys six points ahead, the Scarlets are most in danger of being overtaken for the final Heineken Cup qualification spot.
"Obviously that will be an issue but for us we've just got to go and win our [final] two games, it's as simple as that," Davies said.
"Whatever was going to happen [against Munster] it was always going to be a tight run-in for us.
"The boys are fully aware of that... and we've just got to be hard on ourselves, it's as simple as that, we can't run away from that fact that we're in a bit of a dog fight now."