Curtis' men will find themselves in the bottom three of the Barclays Premier League before they kick-off against Watford on Monday night should either Newcastle or Sunderland manage respective victories against West Ham and Tottenham on Saturday.
Swansea suffered a huge blow in midweek when Sunderland closed the gap on them to a single point with a controversial 4-2 win at the Liberty Stadium.
Jermain Defoe twice scored from seemingly offside positions while Swans defender Kyle Naughton was unjustly sent off in the first half with the score at 1-1.
The Football Association withdrew Naughton's red card and three-match ban on Friday and the former Tottenham full-back is available for the Watford game.
"I don't think there will be a negative reaction to the Sunderland game," Curtis said.
"There was a bit of anger if anything after Wednesday.
"The players were angry at what had happened and I would hope they would want to right the wrongs after a couple of decisions went against them.
"I hope there will be no long-term affect and certainly I don't sense anything at the moment."
Now in their fifth season in the Premier League, Swansea have mostly stayed clear of relegation danger during their time in the top flight.
They did flirt with relegation two seasons ago but Garry Monk eventually led them to safety after succeeding Michael Laudrup at the start of February.
It has led to suggestions that Swansea might not be as well equipped as some of their rivals for the dogfight ahead.
But Curtis feels his players have the right mentality to scrap and pick up points.
"I've spoken before about the resilience of the modern-day player and I think they have to be like that because there are so many setbacks they have to contend with," Curtis said.
"They'll be fine
They are quite a strong group anyway and now we're looking to the leaders, the likes of Ashley Williams and Neil Taylor.
"They are the type of people that will come forward for us."
Swansea continue to scour the January transfer market with former players Jonathan de Guzman and Scott Sinclair, as well as Everton forward Steven Naismith and Roma striker Seydou Doumbia, among those to be linked to the club this week.
"We all know there's a need to bring fresh players in," Curtis said.
"Our league position tells us we are in trouble and that possibly the only way out of it is that we do bring people in.
"It's all quiet at the moment, but that's not to say there's no frantic deals being done at the moment.
"I'm sure there will be one or two players coming in very soon."
Source : PA
Source: PA