Conor Sammon had given the Rugby Park club an early lead but goals from Phil McGuire, Andy Barrowman and Ian Black were enough to earn the Highlanders all three points.

Jefferies said: "We aren't good enough to have to carry too many players. We played unbelievable football against Aberdeen on Wednesday night but we dropped our standards today.

"Maybe Celtic and Rangers can drop their standards and still win games but we aren't good enough to do that.

"We had only lost to the Old Firm before this and the players should have seen how big a game this was but they have let themselves down."

But the Kilmarnock manager was not convinced that Andy Barrowman, a former Kilmarnock player, should have been given a penalty when he went down after a challenge by Craig Bryson just before half-time.

He said: "There has been a lot said about the penalty in the dressing room and the players were saying that he wasn't touched.

"In fact a few of the Inverness players were even saying in the tunnel that there wasn't any contact. I will have to wait until I see it on TV myself."

Caley boss Craig Brewster was delighted with his team after they moved to fourth in the table with their first home win of the season.

Brewster said: "There was a lot of talk before the game about how good Kilmarnock have been so far this season and I said to my players after the game that that sort of performance shows how good a side we are.

"We lost an early goal and we could have conceded a second but we showed good composure and focus to get back in the game.

"The players deserve a lot of credit for this performance and it is great to get that first home win of the season."

The win means the Inverness club are now sitting fourth in the table but the Inverness manager insists he is not too interested in league positions at this stage of the season.

He said: "It is still early in the season but it is always nice to see your name as high up the table as possible."