“It's not been the best of days but big congratulations to Nico, it's a great result for him”
Mercedes had much more severe degradation than their main rivals Ferrari, Red Bull and Lotus during their race simulation runs on Friday and were also considerably slower.
However, Rosberg said they had improved the car overnight before qualifying.
"We saw in China that we were struggling a little bit more in the race," Rosberg said, "and tomorrow is going to be difficult for us.
"We saw on Friday on the long runs there are other teams that were at least as competitive as us, maybe a bit better, so we need to be cautious.
"The biggest challenge is really the rear tyres, it's just a matter of hoping we have done a better job than the other people and can handle the tyres better but there were some really strong teams on Friday and I'm not sure if we have enough to beat them tomorrow.
"It's between two and three stops. Some teams will try two, maybe us, but that will be really on the edge because the tyres really drop off."
Team-mate Lewis Hamilton qualified fourth but will start ninth after a five-place penalty for changing a gearbox damaged by a tyre failure in final practice.
Bahrain qualifying form
The driver on pole in Bahrain has won four of the eight races to date. The grand prix has never been won by anyone starting below the front two rows
"It's not been the best of days but big congratulations to Nico, it's a great result for him and we can still do something from there," Hamilton said.
Asked if he was concerned he might have another tyre failure in the race, Hamilton said: "For me it is a concern. I don't know exactly what went on. I think they're still investigating to find out exactly what happened.
"It wasn't a very good situation for me, but these things happen. There's no particular strategy that will help me, I will just have to try to gain some positions at the start.
"I like fighting through, it's enjoyable if you're going forwards. Hopefully I will be going forwards."
The race victory is expected to be fought out between Vettel and Alonso, although Lotus's Kimi Raikkonen cannot be ruled out despite starting ninth.
The Finn has showed strong pace at various points of the weekend, especially on race-simulation runs, but did not deliver in final qualifying, in which he said the car was "not fast enough", adding: "It's just one of the places where we don't seem to have the speed."
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