Red Bull, who have won the constructors' championship four years in a row, completed a dismal 21 laps in their new RB10 car, while rivals Mercedes managed over 300 in four days of testing at the Spanish circuit.
"There's a few things we needed to tighten up on our side but nothing major and obviously Renault have some issues that they are tidying up as well," Horner said in an interview with Sky Sports.
"But these cars are so complicated that even small problems can cause big failures."
With a host of rule changes being introduced this season, including new 1.6-litre V6 engines fitted with complicated energy-recovery systems (ERS), Red Bull engine suppliers Renault have struggled with overheating in their ERS.
Adrian Newey, Red Bull's chief technical officer, has gone back to the drawing board in search of a solution and that has left Horner uncertain of how the car will perform at next week's test in Bahrain.
"Obviously, there's quite a bit to do but there's still a fair bit of time before the first race," he said.
"The Bahrain test next week is an important test and we are working very hard at both Renault and Milton Keynes.
"We don't want another test like Jerez but that's what testing is for - you sort your problems out so as not to have them at the races."