After a miserable start to the season, the newly-promoted Saints are beginning to find their feet in the top flight and followed up last weekend's win at QPR with an impressive 2-0 victory over Newcastle on Sunday.
Goals from Adam Lallana and Gaston Ramirez either side of half-time denied Magpies boss Alan Pardew a winning return to his former club, whose victory saw them leave the relegation zone.
"It was probably a better performance than last week," Adkins said. "There was a good momentum about us and we carried that on today [Sunday]. It was a good performance.
"We scored two, but could have scored some more. The crowd were great, the players were great and we got a clean sheet.
"We've been progressing all the way through. Last week I spoke about a growing maturity about the group of players and I think we're progressing well.
"Our confidence has been good since the start of pre-season, but you've got to get yourself ready as quickly as possible to reach the level the Premier League is at.
"The players are doing that and doing that very well at this moment in time.
"We know we're in the hardest, toughest and most desirable league to be in.
"We worked very hard to get here and we'll continue to keep working hard. We have a forward momentum about ourselves."
As well as the three points, Adkins was buoyed by witnessing Southampton claiming their first clean sheet of the season.
Saints' backline has been vastly improved in recent weeks and, having conceded 28 goals in their opening 10 matches, the defence has now let in just two in three games.
"It was good for the team because they work so hard on the training ground," Adkins said of the shutout.
"I thought we played well for a large majority of the season but we have been punished in a big way defensively.
"The lads work hard and there is a growing resolve about the players, a real maturity. You could see that was a good defensive performance yet again."
Saints also impressed at the other end, where Ramirez shone in an impressive forward quartet of Lallana, Jason Puncheon and Rickie Lambert.
"Obviously you've got to get used to it all," Adkins said of Ramirez, who joined from Serie A outfit Bologna in the summer.
"Gaston missed the start of the season as it was before he signed and then he got injured," he added.
"He hasn't lasted the full game today but when he was on the field of play he was exhilarating."
Lambert also failed to finish the match after taking a knock to his leg that will be assessed tomorrow morning ahead of the visit of Norwich on Wednesday.
While Saints will be looking to make it three wins on the bounce in midweek, Newcastle will hope for a response at Stoke.
The north-east side have won just one of eight league games since Pardew signed a new eight-year deal, with injuries seemingly taking their toll.
"We're worried, of course we're worried, because we are Newcastle United and we've really got that dressing room to take into Wednesday night," Pardew said.
"It's not like we can add four or five players from the squad into that group.
"That is our group and they have been soundly beaten today and are going to another tough place.
"We have three days to try and lift the team to try and get ready for another tough game."
The result and performance was hardly what Pardew wanted on his first return to Saints since his sacking in August 2010.
"I thought it was all good up until when it kicked off," he said with a smile.
"It was nice to see some old friends and nice for the fans to give us a nice ovation but obviously it stopped when they got amongst us.
"They did a good job today and we were unlucky as they had a great result at QPR and their tails were up. Their confidence was there and that made it even more difficult for us."