The Welsh side have only had a two-goal lead once in the league this season, in a 2-0 win over fellow strugglers Newcastle United in August.
"At the moment we are at the stage where I think we have to kill off the game rather than hold on to just the one goal," Fabianski told British media.
"If we can score two we can have a lot more control of the game. If we score the first goal, I don't want to say we concentrate on defending rather than attacking, but if we can get the second one it would help us."
Swansea will look to get back to winning ways following draws against West Bromwich Albion and Crystal Palace when they host seventh-placed Southampton on Saturday.
(Reporting by Shravanth Vijayakumar in Bengaluru, editing by Ed Osmond)
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