Dest, 20, scored the second and third goals as Barca extended their unbeaten run in the league to 18 matches to remain within four points of leaders Atletico Madrid.
The United States international, along with left-back Jordi Alba, has benefitted from a more attacking role in recent weeks following coach Ronald Koeman's decision to switch to a back three and deploy wing-backs.
"This system is really good for me and is going well for the team," Dest told Barca TV. "I have more space and I am more involved. I am really comfortable, playing almost as a winger, and it's really easy for me to play in this team.
"I am really happy. It's incredible to win 6-1 against a great opponent. I am also happy to score two goals and to help the team. It was the first time I've scored in La Liga and the sensations are really good."
Dest joined Barca from Ajax for an initial fee of €20 million at the start of the campaign and got off to a good start, impressing in the Clasico defeat to Real Madrid and scoring in the Champions League against Dynamo Kiev.
An injury problem at the beginning of the year ruled him out for several games, though, and subsequently knocked his confidence. However, he has returned to the team in recent weeks, responding to Koeman's call for him to focus more.
In total, he has made 35 appearances in all competitions this season, scoring three goals.
Lionel Messi also scored twice against La Real as he broke Xavi Hernandez's appearance record for Barca, playing his 768th game for the club. There were also goals for Antoine Griezmann and Ousmane Dembele.
"[The performance was] without a doubt the best birthday present I could have received," said Koeman, who was one of three members of Barca's traveling party celebrating birthdays on Sunday.
"I'm also delighted for Griezmann and [Jordi] Alba, who also have birthdays today and both played really well. Scoring six goals against Real Sociedad is incredible."
With 10 games to go, Barca are four points behind Atletico, although the gap could have been down to two if Jan Oblak had not saved a late penalty as Diego Simeone's side beat Alaves 1-0 earlier on Sunday.
"There's a long way to go in the [title race]," Koeman added. "Nothing is going to be decided yet but we've shown we're going to fight until the very end.
"Atletico are strong but against Alaves we've seen how tough every game is -- not just for Atletico, but also for us. And for Real Madrid, who are also there fighting. It's going to be an exciting end to the season."