Kilmarnock manager Gary Locke was satisfied by a second straight victory but stressed that the club was not free from the spectre of relegation.
Locke's side sit 14 points clear of the Premiership's bottom side, Dundee United, following the 2-1 win over Inverness Caledonian Thistle.
They are level with Hamilton Accies and Partick Thistle on 24 points, although both those sides have games in hand.
"I don't think you're ever comfortable," Locke told BBC Scotland.
"We've just got to make sure we play like we did and work as hard as we did today.
"If we do that, hopefully we can get a few results. You're saying we're 11th, but it's really tight down there and, if you can win a few games, you can move up a few places.
"But, if you lose a few, you stay where you are so we're well aware of the task ahead.
"If we can keep playing like that, we're very confident we can turn our season around."
Saturday's win was only their second in 11 league matches, but on the back of last weekend's Scottish Cup win over St Johnstone and a draw with Hearts in their previous league match, it appears they may have turned the corner.
"Our season so far has been pretty stop-start, but in 2016 so far we've shown a bit better consistency, which is good to see," said Locke.
"Two wins now, so hopefully that's going to breed a bit of confidence, but we're still miles away from where we want to be and we're not going to get carried away."
There were lengthy delays during each half and a prolonged half-time as ground staff worked to clear snow from the artificial surface as the officials gave the game every opportunity to finish.
Although his side finished as losers, Caley Thistle boss John Hughes did not seek to use the conditions as an excuse.
"It's a very difficult one," he said.. "I think it's all down to the referee.
"I think he did everything right in terms of stopping the match to brush the lines.
"My only complaint is I would have liked to have known we were going to do that before the game so you can prepare for it.
"But it's neither here nor there. You could see the lines, it was the same for both sides.
"In the last 20 minutes, it started lying a little bit heavily and made it very difficult for the ball to roll and to run with it, but Kilmarnock deserved to win the game."