I don't understand this "Chelsea had no strikers" argument.
Firstly, Mourinho loaned out Lukaku, their best striker. If you aren't happy with your striker, why loan out one who scored 17 goals in the league the season before? Stupid decision.
Secondly, Mourinho never really gave Eto'o or Ba a real run of games. He rotated them so much, none of the two had the time to find some form. He did give Torres a good run in the side, despite being their worst striker. Ba's not the best player in the world, but he scored regularly at West Ham and Newcastle. Arsenal had worse striking options IMO.
Thirdly, Mourinho had two transfer windows to rectify this problem and did nothing. He spent £60 million on players in the two windows, so money was spent.
If Chelsea didn't have good enough strikers, the blame is 100% at Mourinho's door.