In this paper we consider parabolically semihyperbolic generalized polynomial-like maps f. We show that on a certain interval which contains the interval (0,HD(J(f)), the associated topological pressure P(-t\log|f'|) is real-analytic as a function in t. Here, HD(J(f)) refers to the Hausdorff dimension of the corresponding Julia set J(f). Roughly speaking, we obtain these results by showing how to associate to f some finitely primitive conformal graph directed Markov system. This then allows to use a result of Mauldin and Urbanski, which states that for this type of Markov system the pressure function is real-analytic in the relevant range. We remark that our paper extends results by Makarov and Smirnov. Also, note that our method of associating to f a graph directed Markov system is completely different from the method used by Makarov and Smirnov. That is, we do not have to use the construction of Hofbauer towers, nor do we have to introduce a `new Riemann metric' in order to force some proper expansion.