Noah would have taken young specimens, not huge, older creatures. Dinosaurs emerged from the ark to inhabit an entirely different world. Instead of a warm, mild climate worldwide, which existed before the flood, they found a harsh world and climate which soon settled into a lengthy ice age. If climatic hardships did not cause the ultimate dinosaur extinction, man's tendency to destroy probably did. This is just a brief and incomplete overview of the Biblical perspective for how dinosaurs fit into earth history and how they became extinct.
Many questions remain unanswered.
However, Christians do not need to feel shy or foolish about standing on the Word of Scripture in their understanding of the world around us. Life, including dinosaurs, are readily explained from a creation perspective because there is ample scientific evidence to support the Biblical record. Evolution serves as the foundational basis for the religion of humanism and atheism where man is autonomous, accountable to no one but himself. These religious beliefs are popular because they have no need for God, no need for His rules, guidelines, or moral standards. Creation serves as the foundational basis for Christianity which acknowledges that all things were created by Jesus Christ, that we live in a fallen universe, and that it will be restored to perfection in the future.