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 and took the lead 64 minutes in when Morgan Schneiderlin made their dominance count by nodding home from close range.
However, the Premier League's leakiest defence was founding wanting once more as goalkeeper Paulo Gazzaniga's poor pass to Maya Yoshida was picked off by one-time Southampton academy graduate Nathan Dyer, who punished the hosts.
''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.
''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.''
Adkins took his side away for a break in the build-up to the game and shuffled his side around in a bid to take the three points.
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.
''I think we did well in the first half. We did not create much today, to be honest, and in the second half they put us under pressure.''