Dimitar Berbatov's eighth-minute strike looked enough for the Whites to secure victory on a wet and blustery afternoon at Craven Cottage.
However, Rickie Lambert's penalty five minutes from time earned Southampton a point.
"The players have shown a good resolve," Adkins said. "When you come away from home to leave with something is important.
"If you look at the second half I think we've had a good amount of possession, a few opportunities.
"We scored a penalty but I think in the second half we looked like the team likely to go on and win the game.
"It is about picking up results. At the start of the campaign we played eight out of the top 10 in our first 10 games of the season.
"The goals against column consistently now is more reduced to what it was.
"There's a togetherness about everybody and maybe we are not getting punished like we were at the start of the campaign but there's a growing experience.
"The players are working very hard for each other and we are maturing all the time."