Caley Thistle boss Butcher is tipped to be confirmed as Pat Fenlon's successor this week and he would have had mixed feelings as he looked on from the Easter Road stand on Saturday, after opting not to take his place in the opposition dug-out as talks continue.
Goals from Nick Ross and Billy McKay secured the three points to take Inverness into second spot in the Scottish Premiership, with Williams branding his own side's first-half display as "disgraceful".
Williams said: "It boils down to professionalism. As a group of players you can't expect to play a game the way that we did and deserve to get anything out of the game.
"It was made clear to all of us, and we made it clear to ourselves, that we had a point to prove. Inverness obviously had a point to prove.
"We are auditioning, if you like, for a new manager coming in.
"It's about the opinions that you give him of yourself. I don't think we did ourselves any favours whatsoever."
The players were unaware that Butcher was in the stands, with reports before the game indicating he would not be attending the match.
Williams added: "Me, personally, I wasn't made aware of it.
"But whether the new manager was going to be in the stand or not, you are picked to put a performance in on the park.
"The second half was better but the first half was disgraceful."
Williams believes the Hibs players have been affected by the speculation since Fenlon's departure on November 1.
He said: "In all honesty, I think a few of the boys were playing with that in mind instead of going out and expressing themselves and doing what they are good at doing.
"Instead of just playing their natural game, they got caught up in all the furore of a new manager coming in."
He added: "I'm captain while James [McPake] isn't in the team and I feel a responsibility.
"As a player, and knowing the boys and what they are capable of, I'm angry and frustrated at the fact that we have got a hell of a lot more to show and we are not doing it.
"We haven't scored in four games and we've conceded six in those four. It's not good enough.
"The boys are all frustrated. They do know they haven't performed to their abilities.
"But if you were to ask a fan who came through the turnstiles and paid good money, out of those two 11s who would they rather be following, it would be Inverness.
"We shouldn't have that as players. We are playing for a big club and we are playing for all our futures. We should show a lot more."
Inverness assistant boss Maurice Malpas took charge of team affairs for the day.
He said: "I thought the boys were fantastic. There was a lot of hullabaloo during the week about what was happening and what wasn't happening.
"It was difficult but the players showed what type of pros they are and what type of club we are."
- Sports & Recreation
- Pat Fenlon