A winless run of seven Premier League games has seen Michael Laudrup's Swans drop to within three points of the relegation zone.
Tottenham, meanwhile, have yet to lose in the league under Tim Sherwood and are firmly in the mix for a top-four finish.
Winger Routledge feels Swansea have deserved more from some of their recent performance, but the 29-year-old knows they must start picking up points soon.
"It's an eye-opener to show what happen if you don't pick up points in the Premier League. It can suck you in," said Routledge.
"It's down to us to respond and pick up as many points as we can between now and the end of the season.
"It's the closest we've been to the bottom, but I don't think that's a reflection of our performances. They've been okay, we just haven't been able to pick up points at the right times.
"Hopefully we can keep performing and the results will turn for us.
"Don't be mistaken, we're in two cups, but the main goal for the season is to remain in the Premier League."
Swansea's cause has not been helped by an injury list including first-team regulars Michu, Michel Vorm, Nathan Dyer, Jonathan de Guzman, Jose Canas and Pablo Hernandez.
And Routledge has warned his team-mates they need to raise their game to compensate for their absentees.
He said: "It's going to be a tough game, everyone knows that.
"Tottenham are a good team that are picking up points at the moment.
"We've picked up a few injuries all over, so it's down to everyone to put in five or 10 per cent more.
"We'll keep performing and hopefully we can pick up some more points on the weekend."
Swansea have yet to feature heavily in a battle to avoid relegation, having been comfortable mid-table finishers in each of their first two seasons in the Premier League.
Routledge admits there have been increased expectations this term after last season's Capital One Cup success, but feels the current run is just a blip.
"Managing expectations is difficult, especially after the last two seasons," said Routledge. "But I feel it is in our own hands about what happens between now and the end of the season.
"It's been a great couple of years, and this is a bump in the road. We have to show our character to get out of the situation we find ourselves in."