Redknapp has been charged with the task of leading the Saints away from the dropzone following his controversial switch from Portsmouth earlier this month.
But he was given a stark reminder of the size of the task as the south coast side extended their winless run to six matches and were lucky to escape with a point.
Redknapp made five changes to his team following their 5-1 hammering at Tottenham last weekend. Sought after striker Martin Cranie was restored to the starting line-up in a 3-4-3 formation, and he was paired with Kevin Phillips and Peter Crouch up front.
Redknapp also gave midfielder Matthew Oakley his first appearance since rupturing his knee ligaments in September last year.
But it was Charlton, buoyed by a run of three successive wins, that made a bright start and they could have been two goals in front inside 14 minutes.
Midfielder Jerome Thomas should have opened the scoring in the 12th minute after Danny Murphy had sent him clear.
However Thomas, who netted in last weekend's 2-1 win over Fulham, put his shot straight down the throat of Antti Niemi.
Oakley was called into action for the first time a minute later when he blocked Talal El Karkouri's goalbound shot after Niemi failed to deal with a Murphy corner.
The travelling Charlton fans thought their side had opened the scoring in the 14th minute when striker Shaun Bartlett headed against the crossbar.
Saints only half-cleared another Murphy corner and when Dennis Rommedahl lofted the ball back into the penalty area. Bartlett's shot cannoned back off the woodwork from six yards.
Hermann Hreidarsson gave Southampton a scare in the 20th minute when he put a free header wide of the left-hand post from Murphy's free-kick.
Southampton finally threatened the Charlton goal for the first time six minutes later when Danny Higginbotham's close-range effort was palmed away by Dean Kiely after Paul Telfer's corner had caused confusion in the visitors box.
Crouch was denied a fourth goal of the season when his right-footed power drive was deflected away by El Karkouri 12 minutes before half-time.
But Crouch should have made amends in the 43rd minute after Oakley, who understandably looked short of match fitness, had breached the Charlton defence.
He floated in a pin-point centre from the byline but Crouch mistimed his header and the ball sailed harmlessly wide of Kiely's right-hand post.
Redknapp used three substitutes in the second half in a bid to grab that elusive first victory with Anders Svensson, David Prutton and belatedly Brett Ormerod all being called from the bench.
It was Ormerod who came closest to winning the match for the hosts with a late header. Phillips did well to hook a Telfer corner across goal only for Ormerod to head agonisingly into the stand four minutes from time.