Palace host the struggling Saints on Sunday.
Chalobah said, “We want to just to push on, so we've got to take it game by game and focus on the next game, and forget about what happened last season.
“We're in the present now, and we've got to just be ready for every game. As we know, every game in the Premier League is very tough, and we'll be up for it.
“(As a defensive unit) it's been really good. We’ve grown that relationship between each other, I understand, and that's what happens when you play week in, week out with each other.
“Marc (Guéhi) is going to be a big miss (against Southampton with suspension), but we've got players that can come in and do their job also.”
On the draw at Bournemouth, Chalobah reflected: “It was a great battle. We knew, the danger that they posed, the momentum they had as well, winning a lot of games, and we knew what we were up for.
“That’s the relationship we've built between us defenders, and I think we're getting stronger and stronger every game. What Bournemouth could pose, we were ready for that, and the teams that have come here, obviously, have struggled against them, but we were up for the battle, up for the fight.
“It was a physical battle from both teams, and away from home, for us, it was a good point, and now we’ll focus for Sunday.”