The Cumbrians bounced back from last week's heavy televised defeat at Brentford with a last-gasp 3-2 win over Yeovil at home on Saturday, but only 4,265 turned up to watch at Brunton Park.
"We were very aware that many of the fans who had stopped coming to watch us had seen that performance [at Brentford] on their TV screen," Abbott told the club's official website.
"They will have switched it off thinking 'I told you so' and it will be very hard to win them over. It's those same fans who didn't see us beat Sheffield United, or Yeovil away, or the fantastic game at Preston, their only impression of us was a very, very bad display."
Abbott added: "We had 4,265 people here on Saturday and we needed every single one of them to help us beat Yeovil, but I honestly think some of them came here to grumble, even before we'd kicked off, because of what they'd seen on Monday night.
"They needed us to prove to them that we deserved their support and it was hard work. We had to make sure we performed and by the time we got to full-time I think we'd achieved that."
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