Gallacher pulled off a series of tremendous saves but was finally beaten by Sam Stanton in the closing minutes as Hibs secured a vital point in their bid to avoid having to enter the relegation playoffs.
They now need to beat Ross County on Tuesday night to secure their Scottish Premiership status for another year.
Butcher said: "I hate him, every game he plays against us he does well.
"What a game that was. He just makes wonderful saves, he's a top keeper. I'm going to make him retire I think.
"I'm going to check my tyres to see if there is a cat underneath them; I don't think anyone has broken any mirrors. What a game that was.
"Maybe our luck is turning though, I did go for a walk this morning on North Berwick golf course and I found two golf balls. I've got to go and find four or five next time to get a win.
"A win on Tuesday night and we're safe. The boys could not even give themselves a round of applause after that because they were so tired. They showed a lot of character and a lot of guts, they just kept going."
Partick boss Alan Archibald thought his side would have been worthy winners, having taken the lead early on through Kris Doolan - a win over Hearts on Wednesday would see them close to survival.
Archibald said: "We had a break away in the first half that could have made it 2-0. Chris Erskine should have scored and that could have been enough at that point.
"We knew at half-time they would throw everything at us and we thought we could pick them off. We were maybe a bit careless with that final pass.
"Because we were leading the game it feels like a defeat but it was a positive performance and positive result. We go into Wednesday with confidence and a win then should make us safe."