Visiting goalkeeper Kelvin Davis pulled off a string of fine saves in the first half while Charlton's Nicky Weaver was called into action in the second.

Parkinson, who took over from Alan Pardew after he left the club following last weekend's 5-2 Championship defeat by Sheffield United, remains confident the club will stay in the second tier.

"I think we have a very good chance [of staying up]," he said. "We have to remind ourselves of the position we are in.

"We are going to need the desire and discipline to win matches and keep clean sheets, and we showed that today.

"I thought [this match] was a big improvement. I said to the boys afterwards, especially the new players, from where we've been, getting beat 5-2, that's a big improvement.

"In the first half we were terrific and their goalkeeper has had a fantastic 45 minutes, and Southampton probably controlled much of the second half.

"We ran out of steam a little bit after the effort we put in over the first 45 minutes and our goalkeeper was called upon in the second half.

"In terms of the drive and determination of the team and the way we attacked the game, I cannot fault that.

"Confidence does not come over night. It is built brick by brick and we have to build now. The confidence is slowly coming back.

"This was the first clean sheet in 13 games and we are looking to keep the ball out of our net."

Charlton almost took a first-minute lead but Mark Hudson was unable to direct his effort from Hameur Bouazza's free-kick on target.

Keith Gillespie then fired wide after a surging run from fellow loan player Jay McEveley before Bouazza had two shots off target.

Gillespie was again at the centre of the action four minutes before half-time when his strike from 15 yards drew a fine save from Davis.

Minutes later, Davis made two more excellent stops. First he denied Bouazza from point-blank range before saving smartly from Deon Burton's over-head kick.

Southampton's best chances of the first-half fell to Adam Lallana and Bradley Wright-Phillips, who both fired narrowly wide, while Rudi Skacel's effort was straight at Weaver.

After the restart Southampton had a chance through Lallana but the England Under-21 international shot wide.

At the other end, Bouazza blazed over and then dragged another effort wide of the post.

Southampton enjoyed the better of the second period and Charlton had Weaver to thank for earning them a point when he pulled off a late double save.

Saints manager Jan Poortvliet was happy to come away with a point.

He said: "My goalkeeper was special in the first half and we were special in the second.

"We created some chances, which maybe we should have taken, but I'm very happy with the draw.

"A clean sheet is important because we are growing as a team. We now have to start winning at home.

"Two clean sheets in a row I can live with. We did a good job today. Charlton had a lot of loan players and showed a lot of fighting spirit.

"We never knew what it was going to be like coming here with a caretaker manager coming in."