The former England captain made a positive start to his tenure at Easter Road but says he is now feeling the heat from the Hibs faithful.
Saturday's shock William Hill Scottish Cup defeat to Championship outfit Raith was the fifth match in succession Butcher's side have failed to win.
A few raging fans even posted off messages highlighting their displeasure but Butcher has already replied personally, vowing to turn the results around, starting with Saturday's Scottish Premiership visit of Ross County.
The former Motherwell and Inverness boss said: "Our recent run is frustrating considering the start we had at the club. In fact, I'd use another 'F' word and quite a few others.
"The Raith defeat has taken quite a bit of the gloss off of that start but hopefully this will be our lowest point and everything now is onwards and upwards.
"The fans have had a lot to suffer over the last few years and it hasn't been great to watch. This season has not been a classic one by any stretch of the imagination.
"But we can give them some hope with a strong finish to the season.
"I've had a few letters from supporters that were pretty damning. I do respond to them - I think they are shocked when I do - because I value their opinions.
"What they have to say is hard-hitting, telling me which players shouldn't be here and what I'm doing wrong. That's fine, because the fans are entitled to their opinions.
"They are frustrated but not as frustrated as me because I'm leading this group and it's my responsibility. We all want to do better so that we have some nice letters landing on the door mat instead of damning ones."