Mark Roberts fired low to give Brian Reid’s men a 24th-minute lead and, despite pressure from the home side, the relegation-threatened visitors held out for all three points.
The result leaves Livi on a run of five straight home defeats – despite four successive victories on the road that have seen them score 14 goals.
Hughes said: “The players are buying in to what we want them to do. We’re just hoping the results come with that and take us where we want to go.
“Today it unfortunately wasn’t our day. I felt we deserved something out of the match as we dominated possession, but you get days like that.
“I felt the performance was very good. It was just in that final third that our final pass wasn’t quite there. I was disappointed with the goal we lost, but I won’t point the finger because I’m asking them to get on the ball.”
Livingston were the first to threaten and Bobby Barr tested Kevin Cuthbert after just three minutes, but the keeper was equal to his effort.
Dean Cummings then saw Cuthbert tip over the bar after he swiped the ball goalwards on 12 minutes, before Keaghan Jacobs fired straight at the Ayr keeper.
The Lions were left to rue those misses, however, as Roberts collected from the right and drilled low beyond Andy McNeil.
Marc McNulty should have levelled for the home side when he was played in one-on-one on 35 minutes, but again Cuthbert denied the home side, before Liam Tomsett nearly doubled the advantage but saw his effort fail to get the better of McNeil.
Into the second half, John Robertson forced McNeil into another fine save on 53 minutes before Livi began to pile pressure onto the sturdy Ayr back line.
Kevin McCann’s effort sailed over and Jacobs again tested the stopper after being slipped in on goal, before McNulty fired straight at Cuthbert all in the space of just ten minutes.
Rory Boulding then came closest to levelling with seven minutes left on the clock, but his effort cracked back off the post to leave the Lions pointless once more against the Somerset Park side.