Butcher's impact since arriving in Inverness was almost immediate on the pitch as with just over a minute gone, Dougie Imrie's daisycutter forced Artur Boruc to parry it away to safety.
Three minutes later and Richie Foran thought he had snatched a debut goal, but he was correctly flagged for offside.
It took Celtic until the 23rd minute to forge a meaningful opportunity and even then it came courtesy of a Caley Thistle mistake. Ross Tokely's poor clearance landed at the feet of Shunsuke Nakamura, who immediately fired a fierce volley towards goal that had to be blocked by the brave Pavels Mihadjuks.
The visitors were enjoying a rare period of dominance as two minutes later Aiden McGeady picked out Georgios Samaras, who might perhaps have feel as if he could have done more to get his head to the cross.
Caley Thistle were battling for every ball and from an Ian Black free-kick on 28 minutes might have taken the lead, but Boruc was out quickly to block a Mihadjuks header.
The Pole was by far the busier goalkeeper in the opening 45 minutes and was quick to berate his defenders after Imrie, playing upfront alongside Andy Barrowman, was allowed time to pick out Foran with a cross on 34 minutes that the Irishman could only guide high over the crossbar under pressure.
Inverness picked up from where they left off in the second half, Black doing well on the angle of the box to curl in an effort that was a couple of yards wide.
Celtic boss Gordon Strachan sent on Jan Vennegoor of Hesselink for the ineffective Samaras in a bid to improve his sides attacking potency, but with an hour gone the visiting team still had not managed a shot on target.
Following a ten-minute lull in proceedings the game burst into life on 76 minutes with both sides coming close.
Firstly, Imrie was inches away from connecting with Russell Duncan's centre, before Celtic went straight up the park and Hesselink did likewise after good persistence by McGeady on the left wing.
Substitute Adam Rooney then forced Boruc to tip his header over the bar as the game moved into the final ten minutes.
With two minutes to go, another Inverness sub Eric Odhiambo, who only signed for the club yesterday, tested Boruc with a low effort that the goalkeeper had to save at his near post.
In a frantic finish, Celtic pushed forward for a winner, but an engrossing encounter ended goalless.