The seventh-placed Easter Road side travel to St Johnstone on Saturday in wretched form, having won only once in their last 11 games to sit four points behind the Perth club, who also have a game in hand over them.
Victory for Saints will consign the visitors to a bottom-half finish this season, with even a draw leaving Tommy Wright's men in the driving seat.
The Hibees boss believes the most important trait missing from his players since he took over from Pat Fenlon last November has been the conviction personified in Tomas Rosicky's second-minute wonder strike for Arsenal against Tottenham last week, which was enough to give the Gunners victory in the capital derby at White Hart Lane.
"I said to the players there is one thing we need more of and that's conviction," said Butcher.
"I highlighted the Rosicky goal for Arsenal against Spurs last week where, bang, as soon as the opportunity came, it was instinctive and he hit it with a lot of conviction and the keeper had no chance.
"I was saying that's the sort of thing we are looking for, instances like that.
"But it could be midfielders or wide-men who have that conviction and you have conviction in your clearances, tackles, all these things in football.
"We need more conviction, no doubt about that, and if we have that I'm sure we will get results.
"But the clarity of our situation is there for all to see. Sometimes when you are on the edge of a cliff, you don't want to jump, you want to get back on to firmer ground, so that's what we want to do.
"We still have a chance. A slim chance, but we still have a chance
"If St Johnstone win, there will be a finality in that, we can't go above them. It makes us focused and determined to have our day."
Butcher will carry out his threat to give some of his young players a start in Perth.
After the 3-1 defeat at Partick last week, the former Inverness and Motherwell boss said: "It will be an interesting team selection next week. I'd rather go with kids and lose if we're going to lose, but let's go with kids, at least they're honest."
Butcher said: "I said last week that there will be changes and there will be changes, so it is about who comes into the team and who stays in the team.
"You say these things to try to stimulate players, to see what reaction you get, but there will be one or two youngsters in the team, that is for sure.
"I'm confident the boys will get together and be strong for Saturday. We have to be. Simple as that."