The Hoops lost 1-0 away to Ajax on Wednesday night to slump to the bottom of their Champions League section and leave qualification hopes up in the air.
However, Dutch defender Virgil van Dijk led the charge against the Staggies with his first two goals - both headers - for the Hoops since signing from Dutch side FC Groningen in the summer for around £2million.
County substitute Ivan Sproule reduced the deficit in the 67th minute, after replacing Marc Klok, but midfielder Joe Ledley, one of five changes for the visitors, returned to top form with a brace of headers too.
The Celtic boss said: "It was a great reaction to Wednesday night and we have preserved our unbeaten (league) record which delights me.
"I thought we played very well.
"There were some good individual performances.
"It is a constant source of frustration that we don't score enough headers from set-pieces.
"You are waiting on one and we get four in one day so it has been a good day all-round and puts pressure on the rest of the teams to keep with us."
The Northern Irishman had special praise for his two scorers.
He said: "He (Virgil) has got that in his game.
"He has been a bit off in his timing so we have worked with him on that and we are delighted that he has been able to come up with two.
"He is a special player, he is playing exceptionally well at the minute, as are a number of them.
"Joe has had a relatively stop-start beginning to the season.
"He has had a few injury problems and he is just starting to look more like himself."