Sunderland head to the Liberty Stadium on Wednesday night knowing that victory would take them to within one point of Swansea in the Barclays Premier League.
Swansea are currently two points above the relegation zone but would drop into the bottom three if Newcastle beat Manchester United on Tuesday night.
"It's a big game, yes," said Curtis, in charge of a league fixture for the first time since his appointment as Swansea manager was confirmed until the end of the season
"But I wouldn't call it a must-win game at the moment.
"A must-win game is if you need to win your last game of the season to stay up.
"But we need to win games sooner rather than later, and the longer you go without a win the pressure starts to build.
"We know it's a big game against a team just below us in the league, and we know the significance of picking up three points against them."
Curtis has won only one of his six games in command since stepping up from a coaching role following the dismissal of Garry Monk last month.
Performances, however, had generally improved until Sunday's miserable FA Cup exit at the hands of League Two Oxford.
But Curtis insists that setback will have no bearing on Swansea's league situation as he prepares to make mass changes once more and recall established players who missed the 3-2 defeat at the Kassam Stadium.
"As disappointed and embarrassed as we were by the performance we have to look forward, and I'm sure there will be a big bounce back," Curtis said.
"I spoke to the players and it's something we can't dwell on.
"It was a bitter blow not to have a cup run because the longer you go it breeds confidence and gives players the chance to play.
"But thoughts go quickly to the Sunderland game
That has to be the case and we will concentrate on what is going to be a massive game."
Veteran midfielder Leon Britton is set to make his 500th appearance for Swansea, over 13 years after making his debut while on loan from West Ham.
Britton subsequently made a permanent switch the following summer and, apart from an six-month spell at Sheffield United from August 2010 to January 2011, has spent his entire career since in south Wales.
"It's hard to find words to describe how important he has been for the club," said Curtis.
"From the day he walked into the club he has been an inspiration to everybody.
"When Leon's playing the team is a better team and I think he sets the tempo.
"He's the one that sniffs out danger and stops it at source.
"He's been a huge part in the rise of the club in the last 10 or 12 years, and to play 500 games for one club in the modern era is a huge achievement."
Source : PA
Source: PA