Two key challenges in underlay dynamic spectrum access (DSA) are how to establish an interference limit from the primary network (PN) and how cognitive radios (CRs) in the secondary network (SN) become aware of the interference they create on the PN, especially when there is no exchange of information between the two networks. These challenges are addressed in this paper by presenting a fully autonomous and distributed underlay DSA scheme where each CR operates based on predicting its transmission effect on the PN. The scheme is based on a cognitive engine with an artificial neural network that predicts, without exchanging information between the networks, the full adaptive modulation and channel coding configuration for the primary link that is received with highest power by a transmitting CR. By managing the effect of the SN on the PN, the presented technique maintains the relative average throughput change in the PN within a prescribed maximum value, while also finding transmit settings for the CRs that result in throughput as large as allowed by the PN interference limit. Simulation results show that the ability of the cognitive engine in estimating the effect of a CR transmission on the full adaptive modulation and coding (AMC) mode leads to a very fine resolution underlay transmit power control. This ability also provides higher transmission opportunities for the CRs, compared to a scheme that can only estimate the modulation scheme used at the PN link.