The match at Ross County's Global Energy Stadium was halted at half-time with game still goalless following a floodlight failure.
Butcher - whose side host Dundee United in the League Cup quarter-finals on Tuesday night - said: "We are still angry about the game on Friday night. Not so much about the floodlight failure - there was nothing we could do about that.
"However, the fact is that we had two bookings in the game - Ross Draper and Gary Warren - and these bookings carry forward. They are part of the disciplinary process now and they will count.
"If it was a red card, it would also have counted and I would totally agree with that - but not bookings.
"Nothing else counts in the game - the score doesn't count and if someone had scored a goal, it wouldn't have mattered either. But these bookings count.
"So in effect for both ourselves and Ross County, our league season will be 38-and-a-half games. How can that be fair?
"From a fairness point of view, these bookings should be scrapped but according to SFA rules they have to be upheld. I will be pushing hard for a change in the laws because it's absolutely ludicrous that players booked in an abandoned game tally up."
Tuesday's last eight clash with the Arabs offers Inverness the opportunity to make up for last season's semi-final defeat to Hearts at Easter Road.
The Highlanders missed out on the first ever major cup final when they lost out on penalties but Butcher wants his men to use the pain of those memories to inspire themselves towards victory.
"We want to go further than last year," stated the former England skipper.
"It was heartbreaking to go out on penalties against Hearts. We were angry because we thought we should have gone through over the 120 minutes.
"It was really disappointing but we can use that anger and turn it into a winning display against Dundee United and help get ourselves though to the semis.
"A lot of teams will fancy their chances with Celtic being out. There will be a name going on the trophy that wasn't expected to be there at the start of the competition when it started out. Hopefully it could be ours.
"Celtic going out has spiced things up. Anyone can beat anyone in the SPL. There has to be a winner on the night. It's not about wonderful football or making 20 to 30 passes.
"It's about making sure you are the winner when the ref blows the final whistle."