Goals from Adam Lallana and Gaston Ramirez either side of half time handed Adkin's men back-to-back wins - following their 3-1 success at QPR last weekend - and saw them move out the relegation zone.
"It was probably a better performance than last week," said Adkins.
"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.
"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."