The former Inverness Caledonian Thistle boss replaced Pat Fenlon at Easter Road earlier this month on a three-year deal.
Handling believes that Butcher and his assistant Maurice Malpas have boosted the squad's confidence since their arrival.
"Terry and Maurice are great motivators. They are very good at what they do - they can motivate anyone," Handling told Football365.com.
"They have all these different ways of getting us positive and confident. We've had a few meetings with him as a group where he has sat us down and asked us questions about how we feel about certain things. He's also played us a few DVDs which are aimed at motivating us as well.
"That confidence is crucial because without it, you just won't play well. But he is already starting to put that back into the squad and we all appreciate it."
Hibernian face Ross County in the Scottish Cup on Saturday.