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 afternoon.
"It was probably a better performance than last week," Adkins said. "There was a good momentum about us and we carried that on today. 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."
Adkins added: "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."
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.
"The players are doing that and doing that very well at this moment in time," Adkins said. "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."
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.
The result and performance was hardly what Pardew wanted on his first return to Saints since his sacking in August 2010 and he said: "We have three days to try and lift the team to try and get ready for another tough game.
"I thought it was all good up until when it kicked off. 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."
Source: PA
Source: PA