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 at home to Newcastle.
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."
"We scored two, but it could have been 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 in the group of players and I think we are 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 very well at this moment in time.
"We know we're in the hardest, toughest and most desirable league.
"We worked very hard to get here and we'll continue to keep working hard."