Ashley Williams says the Swansea players have accepted more responsibility since head coach Francesco Guidolin was admitted to hospital.
Swansea recorded back-to-back Premier League wins for only the second time this season as Gylfi Sigurdsson's sixth goal in 10 games saw off relegation rivals Norwich at the Liberty Stadium on Saturday.
The victory came only three days after Swansea's shock 2-1 success at Arsenal, but Guidolin missed both games with a chest infection which he is still being treated for at a London hospital.
First-team coach Alan Curtis was in charge of team affairs on both occasions, but Williams said the onus has been on the players to respond to Guidolin's absence.
"With the gaffer not being here we've had to step up a little bit and try and make it smoother on game day and in training," Williams said after Swansea had put nine points between themselves and the drop zone.
"Going to London for a week [for the Tottenham and Arsenal games] has brought us closer together as a squad and we can't really ask more from two games.
"The gaffer's not been well and hopefully the two wins have cheered him up from his hospital bed.
"Before he went into hospital he set us up for the games and he's been brilliant since he came in.
"Hopefully he will be back in Swansea soon, fit and well and back on the training pitch."
Guidolin is due to leave hospital on Monday and Curtis said he expects him to be back in the dugout for next weekend's trip to Bournemouth following a couple of days' rest.
The Italian will return to a training ground buoyed by successive wins and probably needing six or seven points from their remaining nine games to secure a sixth season of Premier League football.
"We've put a bit of distance between ourselves and the bottom four, but we need to keep pushing on," said Williams.
"The season doesn't finish today and 33 points doesn't get it done, so we just need to keep going and pick up more points.
"We said that if we'd beaten Arsenal and didn't follow it up against Norwich then the win in midweek would count for nothing.
"So to get back-to-back wins, a clean sheet and grind out a 1-0 win is perfect for us.
"We played better on Wednesday night, but it doesn't really matter at this stage. It's all about getting the results and the points."