The former Netherlands international failed to keep his side in League Two following their 2-0 defeat to Northampton, leaving the club out of the Football League for the first time in eight years.
"I will have to evaluate things with the chairman in the coming weeks," Davids told BBC Late Kick Off London. "I definitely want to be at Barnet.
"It is sad because League Two was a fun league to play in. I had a great time and it is sad it had to end this way."
Davids became head coach at the end of December after initially joining the club as joint-coach.