Martin Barkley, the outgoing chief of the Mid Yorkshire Hospitals Trust, said a serious shortage of surgeons was the more pressing issue.
The government announced an extra £5.4billion for the health service on Wednesday, to help hospitals carry out a backlog of medical treatment which has built up during the pandemic.
But Mr Barkley, who's run Dewsbury, Pontefract and Pinderfields Hospitals since 2016, said the problems ran deeper than cash.
He told a trust board meeting on Thursday, that "money has not been a constraint" on carrying out planned operations this year.
He added: "The largest constraint has been theatre staff. We’ve got 25 per cent vacancies in that department.
"We’ve more than enough theatres.
"It’s not clear to me how just money will solve the problem.
He added: "It’s going to be really difficult to achieve the activity levels we want to achieve."
The trust was forced to suspend all non-emergency surgery at Dewsbury Hospital last month, because of overcrowding.
High volumes of patients attending A&E at Pinderfields Hospital in Wakefield and a shortage of beds across the the three sites contributed to the problems.
However, the trust chief suggested that surgery may resume at Dewsbury "imminently", with one of the hospital's wards now described as being "empty".
Mr Barkley was later given a warm round of applause from colleagues, as he attended his last public meeting before his retirement later this month.
Local politicians and NHS staff have praised him for making many improvements to the trust during his time in charge, having taken over a deeply troubled organisation in 2016.
Local Democracy Reporting Service