The visitors played the final 16 minutes with 10 men after defender Sean O'Hanlon was dismissed for two bookable offences.
Centre-half O'Hanlon was shown a second yellow card in the 74th minute for a foul on Joe Ironside, after an innocuous first-half booking.
Cumbrians' midfielder Liam Noble came closest to winning the game for the visitors, but his 44th-minute drive came back off a post.
"I'm disappointed we didn't get three points, to be honest," Abbott said. "The performance and chances and general play, I thought we were excellent.
"It was only the last 15 minutes when the referee decides to get involved in a game he doesn't need to get involved in and stops our momentum.
"But, chances first half, we thought we should have come in one-nil up and if we kept playing like that we'd get a goal in the game."
On O'Hanlon's dismissal, Abbott added: "It's about time the referees come out and answer the questions you're asking me.
"If he's going to get sent off for that, there could've been eight sendings off in a game where there shouldn't have even been a yellow card; it was a terrific game with spirit and determination and not one bad tackle in the game.
"I don't even want to talk about him (the referee) because he was that bad that I don't think you'd ever have an 11 v 11 if that's what you're getting sent off for. Technically, it's probably correct, but practically, he wants shooting."