Gaston Ramirez exploited a lucky bounce to fire the hosts ahead after 59 minutes at St Mary's, but Carroll equalised seven minutes later with an equally fortunate deflected free-kick.
Allardyce is yet to receive an extension to his current contract, which expires in the summer, but after seeing his side move on to 38 points, he is confident a new deal is not far away.
He said: "It is closer. Hopefully we can get it tied up soon so we can get on with pre-season work. When it is all tied up, we want to put pen to paper as soon as we can.
"I will have a chat with the owner. Let us just get this season over and done with."
West Ham, who sit 12th in the Premier League, moved seven points clear of the relegation zone at St Mary's and with four of their remaining six league games being at home, Allardyce is predicting a strong finish to the season.
He added: "The point is very satisfying when you have gone 1-0 down. It has brought us a point closer to the magic 40.
"I find it highly unlikely that we won't pick any more points up. We won't lose six on the bounce.
"We go into the last six games - four at home, two away - and if we can continue to perform like we have at home, we will pick more points up. We should finish strongly this season and pick more points up."
Away form has proved an Achilles heel for West Ham this season and although Allardyce was happy with the draw at Southampton, he once again felt they lacked a goal threat.
He explained: "In the end we were more than comfortable but, again, our away goals has been our big problem. We looked like we weren't going to score yet again.
"We are making the chances and they were chances that you would ask the players who got them to convert. We need to make sure we convert more of the chances we create.
"In the end we have got a 1-1, so we are happy. With such a poor away record it is very pleasing to pick the point up at the business end of the season. We are in a nice position in the league now."