This work discusses a pricing-based distributed network power minimization approach for multicarrier networks. The aim is to allocate the powers of transmitters over available carriers, such that all Transmitter-Receiver (Tx-Rx) links meet a rate constraint and the total transmit power of the network is minimized. We seek to find a local optimum of the total transmit power by solving the Karush-Kuhn-Tucker (KKT) optimality conditions in a distributed way. Each transmitter minimizes the weighted sum of its powers over carriers, subject to a fixed rate constraint, by a weighted waterfilling principle. The weights consist of interference pricing terms received from interfered links. The exchange of information among the Tx-Rx links enables a non-selfish response that reduces mutual interference. Performance is evaluated in a Small Cell Network (SCN) and compared to a baseline non-cooperative approach. The results show that the proposed algorithm can guarantee a higher rate than the baseline approach, while reducing significantly the total transmit power of the network.