Midfielder Gylfi Sigurdsson believes Swansea can secure Premier League safety with two more victories.
The Swans are nine points above the relegation zone with nine games left, after Saturday's 1-0 win over Norwich.
Iceland international Sigursson, who scored the only goal, told Match of the Day: "I think we'd be happy when we get to 39 points."
Captain Ashley Williams, meanwhile, hopes the win lifted the mood of boss Francesco Guidolin, who is in hospital.
With Guidolin recovering from a chest infection, Alan Curtis was in charge for the second game in succession.
But Williams said Guidolin had "set the team up" for their victories over Arsenal and Norwich.
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"With the gaffer not being here you step up a little bit and try and make it a little bit smoother on game day and in training," said Williams
"He spoke to Curt and he's over the moon with the win so hopefully he's back in Swansea soon and he'll be fit and well and get back on the training pitch."
Earlier this season, Curtis took temporary charge following the departure of Garry Monk.
"He stepped up the last two games, took over the manager spot again and we got two wins," said Williams.
"We're happy for Curt. He did work so hard when he was thrust into that position before."
Swansea's next game is at Bournemouth on Saturday.
"There's no point going there and folding and thinking the job's done because it's not," said Williams, who scored the Swans' winner at Arsenal.
Watching Match of the Day 'not too bad' now
Williams said Saturday's game was tense, lacked quality, was full off effort from both teams and "not the best game of football".
He added: "We're just happy that we ground out a win. We played better against Arsenal.
"Things can look down one minute and you wake up the next morning and everything looks a bit better so it definitely makes nicer reading and you can watch Match of the Day and it's not too bad."