The visitors had Paddy Cregg sent off in the 30th minute for a two-footed tackle on Paul Cairney, just seconds after he replaced the injured Murray Davidson.
Despite their numerical advantage, Hibs failed to create any clear-cut chances, to leave Butcher still searching for his first league win in the Hibs dugout.
Butcher, who replaced Pat Fenlon last month, is well aware of his side's goalscoring woes - Hibs have only one win in their last seven Premiership games, while at home they have only won twice during the calendar year.
Butcher, who was serving a one-match touchline ban, said: "It was very frustrating and you could hear the crowd behind me and hear the comments.
"All you want to do is give them what they want and that's goals and wins.
"They work hard and get into good positions, it's just the confidence of putting the ball in the box or having shots, you can see it's not there.
"Having not scored many goals nor having many wins at Easter Road this year, you could sense there is a fear of winning.
"As soon as the red card came out it was then St Johnstone's best spell of the game. That's something we can eradicate and work on and we will do.
"I'm disappointed with just the point. When we did get through there was Mannus throwing himself at everything."
Hibs had appeals for an injury-time penalty waved away by referee Alan Muir after striker Collins appeared to be caught by Brian Easton.
Butcher agreed with the official as he said: "I've looked it a couple of times and I'm not convinced it was a penalty. It probably could be given but Alan Muir had a good view of it."
After playing for more than an hour with 10 men, Saints manager Tommy Wright - whose side travel to Celtic on Boxing Day - was happy with a draw.
He said: "Hopefully at the end of the season we can look back at it as a magnificent point.
"It's always difficult after going down to 10 men but I thought we limited them to very few chances and I think Alan only had one really difficult save to make in that time."
Wright admitted Cregg could have little complaints over his red card, adding: "Ten years ago it probably wasn't a yellow but he's slightly over the ball and I thought it was a red."