The Japanese driver completed 66 laps in Bahrain today and was the fastest of the four Renault-powered drivers.
But with the French marque's battle to get its 1.6-litre turbocharged V6 engine package working effectively, he admits the team is unable to make serious progress with improving its car.
Bahrain test day two report
This means that Caterham has focused on working with its engine supplier to troubleshoot its ongoing difficulties.
"This is what we have in our hand right now so we have to help them to be able to fight with the other engine manufacturers," said Kobayashi when asked by AUTOSPORT about the engine situation.
"At the moment, we are definitely too weak pace-wise, so we give the maximum chance to them [to work] and thereafter we have to work on our car.
"So we are waiting for the engine system.
"During testing, we meet some other cars and clearly we can see the Mercedes cars are much quicker in the straights, 20-30km/h more and it would mean different braking points, everything, if we had proper power.
"We will see what we can do in a short time. At the moment, we are definitely quite late."
Kobayashi, who also suffered problems with the telemetry system of the Caterham this morning, is finding the power delivery out of slower corners to be a problem.
He is hopeful that this can be improved in the final six days of pre-season testing as currently improvements have been stymied by hitting problems.
But with Renault confident it is making progress, it is hoped that more meaningful work with the car, particularly getting on top of the rear braking-by-wire system, can be achieved tomorrow.
"We had many problems on the engine side," he said.
"This is what we are basically waiting for because we have too aggressive power delivery, which is very difficult to handle under acceleration out of the corner.
"So at the moment, slow corners are very difficult because we don't know how much grip we can get."