That is one of the most challenging questions and one that is asked most often. There are a variety of aspects to the question that must be dealt with separately. Let me begin by stating that there are no simple answers. One could likewise ask a related question that is just as important, although not as interesting to most people, and that is, why do we not find antelope or cows or giraffes with the dinosaurs? While this question does not appear to be as interesting, it really helps us to get at an answer. If we make the assumption that men and dinosaurs were on the earth at the same time, a necessary assumption for Biblical creationists, we must also assume that elephants and giraffes and cows were there as well. That we don't find these animals with dinosaurs either suggests a very different arrangement of life forms on the preflood earth. This is also suggested by a number of other lines of evidence. Some of us are attempting to develop a preflood earth model that takes these observations into account. You can find the current results here.
In any case, many features of the anatomy of dinosaurs suggests that they were much more like mammals than like crocodiles or other present-day reptiles. Some of these features even suggest they may have been warm blooded. If so, they were probably ectothermic homeotherms. That is, their body temperatures were maintained at a more or less constant temperature by a very stable external environment. If so, they may have lived in areas where the ambient temperature approached the body temperature of mammals. In such an environment, mammals would not have thrived, because there would have been no mechanism for them to efficiently shed body heat. The only mammals that might have thrived in such an environment would have been very small mammals with high metabolic rates, and these are the very kinds of mammals we do find associated with the dinosaurs in such deposits. This would certainly not have been a comfortable environment for man. Not only might the likes of T. rex have made poor neighbors, but the ambient temperature in the range of human body temperature would have seemed oppressive, as it does today. On the other hand, it is quite comfortable to ectotherms. I therefore consider it probable that man and dinosaurs lived in very different areas, with different environmental conditions. As a result I would not expect to find their remains in close proximity in the geological column. While this is certainly not the whole answer to your question, it suggests some possibilities for further investigation.
2010 Arthur V. Chadwick, Ph.D.