After an impressive 2-2 draw at high-flying Arsenal, Swansea swept aside Norwich City 3-0 last weekend to move 13th in the top flight - seven points adrift the relegation zone.
With four teams sitting between Swansea and rivals Cardiff City in 18th, Monk's men look to be all but safe from the drop.
However, ahead of Saturday's trip to Hull City, who sit just a place behind Swansea, Monk believes two more victories are needed to make certain their top-flight status.
"We realise the position we're in and we have still got a job to do. For me, I want a couple more wins to ensure we are safe," he said.
"But I also want to win every single game and if we can't (win) then make sure we don't lose."
After Swansea's first two Premier League campaigns ended in finishes of 11th and ninth, as well as League Cup glory last term, this season has been unusually turbulent at the Liberty Stadium.
Following Michael Laudrup's dismissal in February and mixed on-field results, Monk is keen to end this term on a high.
"The players have had a lot of criticism this year and we want to show a message of intent going forward," he added.
"It's important that we finish the season strongly. We've got a job to do and we want to be safe as quickly as possible."
