The result extended the Saints' start to the season to four wins from four - the first time they have ever done that.
"We had to grind out the result in the end but it was a great goal by Guly Do Prado," said Adkins.
"It was a tough game but we have got a gritty mentality.
"It was a good three points but it was a very hard game. We played really well in the first 20 minutes which helped.
"We had to show a different side to our game today. We didn't give ourselves enough quality on the ball. We got the right result, though.
"It was great credit to our players. We have a winning mentality and want to excel in attack and defence."
Millwall boss Kenny Jackett was disappointed his sides lack of quality, after they slumped to their first defeat of the season.
He said: "We can play a lot better than that. We had a co-ordination problem from back to front. I was disappointed with a lot of aspects of our game.
"We showed heart and guts but we didn't play well for a lot of the game. We are capable of a lot better than that.
"We just lacked quality today. The effort and commitment was there but we didn't do ourselves justice at times and I was frustrated."