Generally speaking, the official records of the Korean / Chinese on their own losses were quite reliable, as their registered soldiers had to be accounted for. Though obviously the reports of enemy losses could certainly be dubious, especially in the case where battles happened on sea and most of the bodies could not be recovered. The recorded loss of the allies in Noryang was minuscule, despite the fact that they lost 2 of their primary commanders. 

 It is interesting to note that none of the prominent Shimazu samurais appears to have perished in Noryang, though that has generally held true through out the war and was a reflection of the nature of two sides, the leader of the Japnese were noblemens who carried serious political consequences if they fall in battle, the Ally leaders had no serious status in the courts and were often completely expendable.   

 So if you take the ally records at Noryang on the Japanese losses literally (which obviously can be debated, but I have not seen Shimazu records stating their losses in said battle.), then it's difficult to argue that the Allies somehow lost the fight, the value of Yi and Deng's life simply can not be weighted on the same scale as the prominent Samurai's in terms of political effect. 

 Yi's goal was originally to keep Konishi from escaping, however the entire point of that was to keep as many Japanese as possible from escaping, by sending what appears to be 10-15k Japanese to the bottom of the sea in the ensuing battle if the records were to be believed, it seems that he achieved that perfectly fine. 

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