The season starts in Australia on March 20 but the new qualifying format, announced by the governing FIA last week, will require changes to the software controlling the timing system.
"My guys who do the timing said: 'Mr E, we don't want to be put in the position because we don't think we can get it done properly in time," Ecclestone told the BBC.
He said that the new format would probably be introduced at the Spanish Grand Prix in May instead. The season is due to feature a record 21 races.
Ecclestone's Formula One Management handles the timing software, along with screen graphics and data, and he explained that the changes involved in the new elimination format were not straightforward.
"If you're going to try and explain it to the public properly, it's not just a case of 'Okay, the guy was the last one, bye-bye'," he said.
"We'll have to deal with it. I've told the FIA this and asked them what they'd like to do with it but the bottom line is there's not a lot they can do with it because we do all the timekeeping."
Under the new procedure, the slowest drivers will be eliminated as the three sessions progress rather than at the end of each phase.
After seven minutes of the first session have elapsed, the slowest driver is eliminated with others following at 90-second intervals.
Fifteen of the 22 go through to the next phase, with the slowest eliminated after six minutes. The same 90-second sequence ensues until eight drivers are left.
The final session sees one driver eliminated after five minutes and then one every 90 seconds until two are left fighting for pole position with one-and-a-half minutes remaining.
(Reporting by Alan Baldwin, editing by Clare Fallon)
