Saints 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."
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