Manager Terry Butcher admitted Inverness were not at their best despite beating Kilmarnock 2-1.
Billy McKay lobbed in a sixth goal of the season to win the match after August player of the month Richie Foran had earlier put the visitors in front.
"The lads are very honest about their performances - they didn't enjoy it," Butcher told BBC Scotland.
"We asked the players after 'hands up who played well?' and not one person put his hand up."
Kilmarnock had equalised soon after half-time when Barry Nicholson deflected a Graeme Shinnie clearance beyond Caley Thistle goalkeeper Dean Brill.
"It was a big challenge for our boys and we got a goal virtually straight away," said Butcher
"Today was not our best, yet we still got the three points. We didn't play with any real fluency, little glimpses of it, but we didn't make many chances.
"The players have to realise that teams are going to raise their game against us now, which is a little bit different to what it has been."
In Saturday's early kick-off, Celtic beat Hearts 3-1 to go level on points with Inverness, but the Highlanders restored their three-point cushion with their win in Ayrshire.
Butcher's men have now won five of their six league matches this campaign.
"It's a lovely position to be in after six matches and scoring an average of two goals a game is pretty good," he said.
"But I think the game today showed the boys how much hard work there is ahead of us.
"Billy McKay's the sort of player you don't know what he's going to do or produce. He's got a heart as big as a bucket and he really does work his socks off.
"We had to rely on resilience and strength and a little bit of luck, but sometimes if you're top of the league and winning matches that luck seems to come for you."