The team had roped in South African all-rounder David Wiese as Mustafizur's replacement, and though the Protea was signed for two matches, he had to play four before leaving England to join the Caribbean Premier League in the West Indies.
Sussex will also miss the services of England medium pacer Chris Jordan against Gloucestershire on Sunday as he will be on national duty in the ongoing One-Day International (ODI) series against Sri Lanka.
"We have a couple of people but it is very late in the day; so it is very hard to get replacements," Davis was quoted as saying by bdnews24.com on Tuesday.
"The top players in the world have been signed or are playing CPL or their countries aren't allowing them to play."
"That's the frustration because we have chosen Mustafizur as probably the No.1 bowler in the world in that format."
On June 9, Bangladesh Cricket Board (BCB) physio Bayezidul Islam said it would take Mustafizur at least two weeks to be fully fit but, last week, trainer Mario Villavarayan said the pacer would need another month of rest.
To give the 20-year-old seamer time to recover after the IPL, Sussex gave Mustafizur time off and were hoping to have him by June 10.
Despite the delay stretching more than a week after that, the Sussex coach was still hopeful about getting Mustafizur.
"I spoke to the Bangladesh head coach and he said he would be assessed after two weeks, which is now," Davis said.
Earlier this year, Mustafizur made a brilliant debut in the Indian Premier League (IPL) playing for eventual champions Sunrisers Hyderabad.