Saints had the better of proceedings at St Mary's after a week in which the position of the struggling side's manager had come under increasing scrutiny. Adkins' team responded with character when Morgan Schneiderlin nodded home from close range, but keeper Paulo Gazzaniga's poor pass led to Nathan Dyer levelling for the visitors.
"I think the supporters, players and everyone is having a go for each other, which is the important thing," Adkins said. "We're together as one. Everyone is having a right go, the performance was good. Listen, take the positives. We got a point. We wanted the three and a clean sheet but let's take the positives."
He added: "We got another point on the board. Everyone's together, everyone is working hard. We're 11 games into the Barclays Premier League and we're improving all the time.
"We believe we can give all sorts of teams problems going forward, which we've gone and done this season. We've scored goals. It is the decision-making process at the back [which is the issue]. Today was an improvement in respect of the defensive resolve about ourselves.
"Again, the second half against Tottenham, you throw that into the mix. We were on the front foot and dominated that second half. There is a lot of good things that we're doing and we'll stick at it and keep working hard."
Asked if the result had helped reduce the pressure building at the club, Adkins added: "I think you can see again today that the football club is united and we're determined to be successful here at Southampton.
"We should have had a penalty the other night but didn't get one so at this moment in time things just aren't going are way, but we'll keep working."
Southampton moved up to 19th after a match in which Swansea manager Michael Laudrup was relieved to get a draw. "I am pleased with a point," the Dane said. We knew already before the game that it would be very difficult.
"I think that I said in the press conference on Thursday that we would like to win against Southampton, but they need a win. You could really see that. They gave everything in every moment so it was a really difficult game. I think we can be satisfied with going away from here with a point."
Source: PA
Source: PA