Luke's introduction, doesn't seem like he is claiming he was inspired? When reading the introduction of the Gospel of Luke, it seems very clear that he isn't really claiming to be inspired by God or anything. Rather he is saying that he thinks himself to be more worthy of writing these accounts because he knows the story from the beginning (and probably also because he is educated and not some unlettered person).

Luke 1:1-4 (KJV)
1 Forasmuch as many have taken in hand to set forth in order a declaration of those things which are most surely believed among us,
2  Even as they delivered them unto us, which from the beginning were eyewitnesses, and ministers of the word;
3  It seemed good to me also, having had perfect understanding of all things from the very first, to write unto thee in order, most excellent Theophilus,
4  That thou mightest know the certainty of those things, wherein thou hast been instructed.

What really gets me is his statement:

It seemed good to me also

And another interesting point is that he mentions that many people have written Gospels (which we have only basically 4 now):

Forasmuch as many have taken in hand to set forth in order a
declaration

So I am interested to know, on what basis do the Christians say these accounts are inspired or the word of God? The author sure doesn't sound to come off as that to me, it seems more like a historical account, albeit one that is theologically based, and not something that sounds inspired.
Christians do not believe that the Bible was dictated by God in the same sense that Muslims believe the Quran was dictated to Muhammed. They believe that God inspired the writers, through their own knowledge and personalities, to write the things that God wanted his people to know and remember. Because of this it is possible for an author to write inspired scripture without even being aware of it. It is also true that the early church spent hundreds of years in prayer, in research, and in consideration before choosing the books that today make up the Bible, and the belief is that the process was also inspired by God through his Spirit.

The introduction to Luke does not in any way contradict this. Luke (and it's sister book, Acts) is a carefully researched and collated story of the Life of Jesus and the early church. It is also inspired by God, who worked within the life and thoughts of Luke to bring these writing to fruition. This issue is not restricted to Luke. Many of the other books are letters written by Christian leaders to their churches. It is likely that they did not know of God's working through them, or that their writings would one day become holy scripture. However that does not make it any less true.