Former MotoGP champion Rossi did not break into the top 10 in either session on the opening day in Spain.
"The day is quite negative for us," Rossi admitted. "At the end of the afternoon more or less everybody put on the soft and were able to improve the laptime, I continued with the hard, trying to work with that for the race. It was for this reason I am further back than I expect, but anyway we are not very fast.
"We suffer a lot with rear grip under acceleration, but every modification we try to fix this problem I lose the feeling on the front so we had to go back at the end of the session. We are not fast enough.
"We are quite worried because we have to understand another way to increase the rear grip without losing the front feeling. We will see for tomorrow, because we have some other things to try."
Hayden fared slightly better as he went seventh quickest in the morning and ninth later on, but he was also pessimistic about Ducati's chances this weekend - despite being pleased with his time.
"We were 0.4s from the top, not so far on a long track. We didn't improve as much in the afternoon, the problem is certainly trying to find grip around here," said the American.
"We've made a few small steps with a couple of the things we tried in Barcelona, which seem to be helping. We obviously didn't make the big step we hoped, but a few electrical things Ducati brought for us to try I'm using and they seem to help. Everyone is pretty close though.
"I'm able to get out of the corners and put the power down a bit smoother, but we know it's not half-second stuff. It is more stuff that could make a difference over a race rather than a lap."