This year's sweeping rule changes led to a stunted opening at the Spanish track, with just 93 collective laps being registered on Tuesday. In contrast, the opening day of last year produced a collective 657 laps.
Jerez 2014 F1 test day one report
While Key said such a stuttering start was not unexpected, he warned teams would need to make measurable progress with their machines on day two to avoid falling seriously behind.
Asked by AUTOSPORT when the time teams would start to panic about preparation was, Key said: "If you're getting to the point of only having done a few laps by the end of day two, you do start to get concerned.
"The cars come in with glowing turbos, bits of smoke coming from places; you need to know that is not a problem.
"With only three tests, by the end of Jerez you need to pretty much know exactly what you need to do in order to go to Bahrain in good shape, because you need those two tests to begin to get everything sorted.
Gary Anderson's day one verdict
"Internally we knew it would be very tough because there are so many unknowns - there will always be little glitches that occur.
"Often things can stop you that are actually trivial but end up making you stop for a few hours.
"So if you're not running, stringing laps together and getting everything stabilised - understanding temperatures and everything else - there's another set of possible problems you haven't faced yet.
"Running here you can tackle as many problems as possible before you hit Bahrain."
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Asked what benchmark teams will need to hit to be satisfied they are ready for Bahrain, Key added: "Obviously the more the better, but I think if you can do one afternoon with a couple of decent long runs - 15, 20 laps - and make changes in between and begin to hear what the driver is saying, that gives you confidence.
"You can also get an idea of how well the car is coping with that."