Saints are languishing at the foot of the division after Jones’ first top-flight home game as manager ended in a resounding 3-1 defeat to Brighton on Boxing Day.
Southampton will attempt to snap their four-match losing streak in the league at Fulham on Saturday, before hosting fellow strugglers Nottingham Forest on Wednesday.
Jones, who has only been in the job seven weeks having replaced the sacked Ralph Hasenhuttl just before the World Cup, says his side must not allow a poor position to become a precarious one.
“I think the next game is always vital, you have to bounce back,” he said.
“You want to bounce back from a defeat, you want to bounce back from a poor performance and we’re going to have to do that, we really, really have to do that and we have to do that quickly.
“There is time but we don’t want to leave it weeks after weeks to try and chase something. We know we have to pick up results.
“(The Brighton match) wasn’t good enough, we didn’t defend well enough and regardless of what we did with the ball, or in spells, in moments it wasn’t good enough.
“We have to be better than that and in time we will be.”
Winger Samuel Edozie showed flashes of his potential against Brighton to offer Jones some encouragement for the future.
The 19-year-old, signed from Manchester City in the summer, won his side a penalty and twice went close to scoring on the occasion of his first Premier League start.
Jones believes the teenager, who he brought off the bench in the 3-1 loss at Liverpool on November 12, is an exciting prospect but stressed it will require a collective effort for the club to stave off relegation.
“As a pure talented footballer, he’s wonderful,” the Welshman said of Edozie.
“It’s just a shame that when he does come and do things, we’re two or three down and that can’t happen.
“Everyone has to chip in. I’m not going to solve all of the problems, neither is one player going to do it.
“It’s a collective here and as a club we have to stay up. It’s not what we do now, it’s come the end of May where we are.
“If we’re outside the bottom three come the end of May then we’d have had a successful time to build because all these players will be better having had one year in the Premier League.
“But at the minute we’re learning harsh lessons that are costing us points.”