The resurgent Eagles moved on to 36 points – just three behind 11th-placed Chelsea – with seven games to go following Eberechi Eze’s second-half double at St Mary’s.
Palace grew into the game on the back of a forgettable first half to earn Hodgson a third consecutive victory since he returned to Selhurst Park to replace Patrick Vieira just under four weeks ago.
“I certainly feel more comfortable, with every point you get you feel more comfortable because we’re inching towards a total which we think will be enough for us to stay in the league,” he said.
“We haven’t reached it yet. But if you compare with a month ago when we had 27 points…
“Leicester probably was the one game where we didn’t feel that much under threat. They defended well but they didn’t threaten us in the same way, we dominated that from start to finish.
“But we knew Leeds would be a tough ask and we knew Southampton would, so to come away with six points to say I’m happy with that would be a gross understatement.
“But I’d still like to see us get some more points and I’d like to see this team continue to play in the way it’s capable of playing because it’s been a tough season for the club and a tough season for the players.”
Palace failed to register an attempt on target in a cagey opening period which Southampton edged.
But, like last weekend’s 5-1 triumph at Elland Road, the Eagles were a far greater threat in the second period and went ahead in the 54th minute when Eze volleyed into an unguarded net after Saints goalkeeper Gavin Bazunu pushed away Jordan Ayew’s powerful cross.
Eze quickly doubled the lead with a superb arrowing strike from distance to claim his third goal in two games.
“I enjoyed the second half, where I think we played better,” said Hodgson.
“Southampton were very good in the first. They did all the things I would expect from a team fighting for their lives at the bottom of the league. They stretched our defending capacity to the hilt.
“But luckily we got through that. In the second half, we were able to tweak one or two things and get back to the sort of football I was hoping to see us play for the whole 90 minutes.
“It turned out to be enough because of Eze’s two goals. Goals change games. Eze’s two goals put us in such a commanding position.”
Ruben Selles said Southampton will “keep fighting until the very end” after his side’s relegation concerns were heightened by a sixth game without victory.
Saints, who came close to halving the deficit when Carlos Alcaraz hit a post 16 minutes from time, remain four points from safety and were jeered off at full-time.
“We are disappointed with not getting anything from the game,” said manager Selles.
“We showed where we are in the first half but we didn’t match the tempo in the second half, so the second we concede the first goal we start to make some errors and then after the second goal we weren’t able to come back.
“They (the players) showed the way that they can play and perform. We just need to be us together and more consistent in what we do.
“We know we need to play almost the perfect game to get points and every mistake, every situation that is against us, is punishing us very hard. We will keep fighting until the very end of the season.”