We consider resource allocation under partial feedback in a spatially correlated MIMO link, when the ARQ protocol is implemented at the MAC layer. We propose a design framework, which makes use of results from random matrix theory (RMT), to find the rate as well as the input covariance matrix that maximize the long term goodput. We consider partial feedback in terms of positive/negative acknowledgment bits (ACK/NAK), which comes essentially for free since they are always present in the signaling of the upper layers. We provide explicit expressions of the long term goodput, which, in association with a RMT based approximation of the mutual information enable us to optimize the resource allocation problem. Interestingly, the simulations show that the asymptotic optimization analysis is still valid for MIMO sizes as small as 2x2.