Saints, who had lost just two of their previous 10 games, took a 22nd-minute lead through Jay Rodriguez but the holders hit back with a vengeance to triumph 5-1.
Demba Ba scored twice on his debut for the Blues but Adkins felt Victor Moses' goal which made it 2-1 just seconds before half-time was crucial.
"I thought Chelsea were very good in the second half," Adkins said.
"I think we started the game brightly, scored a very good goal from Jay Rodriguez. It was a good game to watch from our point of view in the first half.
"There was some good football played and the big killer blow came for us on the stroke of half-time with the goal they've gone and scored.
"It is fair to say in the second half, Chelsea demonstrated the good players they've got in the team and to give them credit I thought they were very good and took it away from us.
"What he have to do is put the game to bed, move on and look to the next one.
"We've got a week's recovery and preparation now after a busy fixture period. Hopefully it gives one or two of the lads that have been out a chance to recover and we get ready for Aston Villa."