Southampton boss Adkins disappointed with wasted chances
Adkins rued missed chances which would have turned the match in their favour.
"I think we started the game very well and for the first 20 to 25 minutes we have taken the game to Everton," he said.
"We scored a good goal from a corner and if Jay Rodriguez had gone in and scored (when clean through) to make it 2-0 it might have been a different final reflection.
"Goals change games and with 25 minutes gone the first real passage of play when Everton put a consecutive period of passes together gave them a goal.
"The crowd got behind them, they upped their tempo and the second goal came from a counter-attack which changed the complexion of the game.
"For the 10 minutes before half-time Everton were well in the ascendancy and we weren't able to deal with it.
"Second half we came out with good composure to pass the football and if Gaston Ramirez's little chip had just gone inside the post rather than outside it could have been an interesting final period."