The West Lothian side are without a victory since their famous 2-0 triumph over Celtic in October, after failing to capitalise on their dominance in a goalless draw with Hamilton at Almondvale.
The hosts created the better chances in a poor game played in freezing conditions, with referee Willie Collum the centre of attention.
The experienced official ruled that Jon Guthrie’s first-half header had not crossed the line before waving away Livingston’s second-half penalty claim when Lyndon Dykes’ header appeared to strike Sam Stubbs’ hand.
While the first decision appeared inconclusive, Collum was correct not to award a penalty as the ball struck Stubbs’ stomach, but Holt thought otherwise.
He said: “I’m saying it’s a goal all day long! We don’t have VAR and we don’t have goal-line technology, so it’s part and parcel of the game and the referee has made the decision.
“We don’t cry over it. It’s the same in the second half when I thought there was a handball that could have been a penalty, but we don’t complain about it.
“You’ve got to earn the right to win the game. You’ve got to be proactive and create chances. I thought we were in the ascendancy to try and win the game and had a lot of play in the second half but we needed to be a wee bit braver.
“We knew Hamilton would get a lot of men behind the ball and it might have taken someone shooting from distance and even getting a deflection, but we didn’t take it on enough. If you don’t shoot, you don’t score.”
Other than Guthrie’s header that struck the bar, chances were at a premium in a game which saw Hamilton produce a resolute defensive performance.
But overall the quality of football was poor, with the pitch slippery after being watered before kick-off despite the freezing conditions. An attendance of 1,076 is concerning for a top-flight match and there was little in the way of entertainment for the hardy souls who did turn up.
Accies’ Luke Southwood continued to impress since replacing Owain Fon Williams in goal while Stubbs was dominant in defence and Hamilton manager Brian Rice praised his team’s performance.
“It is a very difficult place to come as many teams have found out in this league,” he said.
“So to come here and get a clean sheet, I am delighted with it. I don’t think there were too many chances in the game. It was a scrappy match but we stood up to it.
“I am delighted with the endeavour shown by the boys. That is one thing my boys will do – they will always work really hard.”