Saints gained a vital 1-0 win at fellow strugglers Aston Villa, albeit through a fortuitous penalty when replays showed no contact was made on Jay Rodriguez before he went to ground.
"That is 11 games now with only two defeats and those were only by a single goal," Adkins said. "We've shown a growing maturity after a baptism of fire back in the Premier League. We've been used to winning at Southampton (in the last two seasons) and we are improving all the time."
It means Adkins' side have taken 17 points from their last 11 games after losing eight of their initial 10 matches back in the top flight following back-to-back promotions.
Adkins added: "Everyone is getting used to this level. A lot of us were in League One a couple of years ago and in the Championship last season.
"We've come a long way and are adapting to the demands of the Premier League.
"The players deserve great credit because they want to improve all the time.
"We've shown we can score goals, have done it consistently all season again, and it was really pleasing to now get a clean sheet at Villa."
Regarding the penalty, Adkins said: "Jay's leg has moved out of the way which is just as well because there would have been contact (from Enda Stevens).
"We don't advocate diving at our club and we probably should have had seven or eight penalties this season that we haven't had. It was a case of what comes around, goes around, that you are due one, that sort of thing. It's a big decision."
Source: PA
Source: PA