Gomez was promoted to CEO after a board meeting on Wednesday and Spanish media reported it was with the support of Spanish bank Bancaja, the club's major creditor owed 240 million euros ($302 million) out of a total debt of around 450 million euros.
Bancaja refused to comment on dealings with a client and Valencia have declined to answer questions about their finances.
"The club is in a very delicate situation. It has to control spending, grow income and sell assets," Gomez told a news conference on Wednesday evening.
Valencia's prize assets include Spain striker David Villa and international team mate David Silva.
Gomez did not rule out player sales when asked.
"Obviously we will consider that type of action," he said. "We have to control costs and the biggest cost in a football club is maintaining a team."
President Vicente Soriano will continue in the post and he denied he had had his powers trimmed with the promotion of Gomez.
Soriano replaced Juan Soler as president last July but his plans to sell the land around the Mestalla to help finance the move to a new stadium that is under construction have not come through.
Valencia, twice Champions League finalists, have been forced to delay payments to their players and construction work on the new stadium has also stopped.
Gomez added: "Before, we had a plan that was based purely on selling the land, now we need to seek alternatives. We need to win back credibility with the financial institutions."
However, Gomez was unable to give a date for when the money owed to the players would be paid. Spanish media reported the figure was 15 million euros.
Valencia's financial problems have been accompanied by a dip in form. They are out of the UEFA Cup and the King's Cup, which they won last year, and have slipped down to sixth in the league.
A recent study of Primera Liga club accounts, based on the 2006/7 figures, concluded that many were living beyond their means and that the global economic crisis would push some towards insolvency unless they changed the way they operated.
Jose Maria Gay, a professor at the University of Barcelona, calculated the combined debt of the 20 clubs in Spain's top division in 2006/7 was 2.78 billion euros.
