Swans were impressive for their draw with Chelsea last week.
Fabianski said: “I wasn't really paying attention to all the doom and gloom.
“There are some really good players and in the second half against Chelsea you could see the character in the team.
“Fans obviously have a right to share their opinion and we respect that, but we need belief from them as well.
“You've just got to keep your head cool and focus on the work. I think if we do that then it will pay off.
“Against Chelsea we showed we are in better shape than some people would suggest.
“We showed we have a never-say-die attitude and if we can keep showing that, as we have done, then we will be fine.
“Everyone is talking about this run of fixtures but we will be prepared for anything.
“When you look at the history of Swansea playing against the big teams. There always seems to be something good happening for us."