The 23-year-old Dutch international, on loan from Real Madrid, failed to join his team mates when they resumed training again on December 27, returning instead a week later, on Monday.
Promoted Hercules are struggling to pay their players and have promised that November and December salaries will be paid by mid-January.
"The situation is clearer than it was before," Drenthe told a news conference, after a number of meetings with the club's directors.
"For now, I am satisfied with the explanations they have given me. All I can do is work hard and, if the boss still wants me, to prove myself on the pitch.
"I understand there are people who think this is about money but it was more about a loss of confidence. If somebody says they are going to do something and then later they don't do it it affects me a lot, and I lose confidence in them."
Drenthe, a rap music fan, had become a cult figure with fans at the Alicante-based club, putting in some of his best performances since he arrived in La Liga at Real Madrid from Feyenoord in 2007.
The supporters gave him a hostile reception when he arrived at Alicante airport on Monday, however, and sprayed threatening slogans on the walls at Hercules's Rico Perez stadium.
Drenthe resumed training on Wednesday and president Valentin Botella said coach Esteban Vigo was free to pick him if he wished.
"(Drenthe) is sorry for what happened. He's young and knows he has done wrong," Botella told sports daily AS on Friday.
"The club have started disciplinary proceedings and he will be fined. This is his punishment and if the coach wants to use him that is his choice. It is up to him now."
