Saints were on course for a second defeat in a matter of days until their hard work paid off five minutes from time.
Rickie Lambert's penalty earned the south coast side a 1-1 draw at Craven Cottage, setting them up nicely for Saturday's trip to Stoke and Arsenal's visit to St Mary's on New Year's Day.
"It's important, especially winning your homes against those around you," Adkins said.
"That's why we were disappointed not to get anything from the Sunderland game just before Christmas.
"To come away and show the great resolve that we have was very positive.
"It's important that there is a positivity about everything we do, there's a desire to do well and everyone's working well for the same cause.
"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."