Media playback is not supported on this device
The Swans, led by Curtis in the absence of ill head coach Francesco Guidolin, saw off 18th-placed Norwich to move nine points above the drop zone.
They are eight points above 17th-placed Sunderland, who drew at Southampton.
"We're still only on 33 points and that is not going to give you safety," Curtis said.
"All we've done is give ourselves breathing space.
"It's a big statement obviously because we given ourselves a bit of breathing space between ourselves and the bottom clubs."
Swansea's 1-0 win over Norwich followed Wednesday's 2-1 victory at title contenders Arsenal.
Iceland midfielder Gylfi Sigurdsson's second-half strike was enough for the Swans to beat the Canaries, who have not won away since December.
The goal was a rare moment of quality in an otherwise cagey game.
"I thought we were really poor in the first half," Curtis admitted. "I thought it was a poor game to be honest.
"I think both teams just got caught up in the tension and the enormity of what the games mean to them.
"As a spectacle, I thought it was quite poor. In the second half, we controlled it for long periods.
"The goal was probably one of the best moves of the game. Gylfi finished it really well.
"Then we were hanging on at the end, not necessarily through some good play by Norwich, I must thought we got a bit tense at the end.
"Possibly they could have equalised at the end, although we did deserve it, over the second 45 minutes."
Curtis said the Swansea camp had received a message of congratulations from Guidolin, who remains in hospital in London as he recovers from a chest infection.
"It's bound to give him a huge boost," Curtis continued. "As far as I know he is due out of hospital on Monday.
"I would imagine he needs to spend a couple of days at home. Hopefully towards the middle or end of the week he will rejoin us.
"Hopefully he will be with us (for the match) next weekend."
Swansea next travel to face Bournemouth on 12 March, before hosting bottom club Aston Villa at the Liberty Stadium.
First-team coach Alan Curtis believes Swansea City's back-to-back Premier League wins have given them "breathing space" over their relegation rivals.