This podcast covers the topic pretty closely and is a great interview with one of the old pilots of the Concorde. From his accounts the Air France Concorde crash was the last straw that lead to its shut down but was not the only factor.
The Concorde itself was, in its prime, a very profitable airplane and made BA and Air France loads of money when they flew it. However the plane was extremely costly to operate. Due to its supersonic nature the air frame saw a great deal more fatigue than a subsonic plane and it became not only expensive but time consuming to maintain the aircraft. All the while regular jets got bigger while the Concorde did not. Consider that the plane had a 100 person capacity while jumbos kept getting bigger. In turn the smaller margins jumbos made per person were beginning to catch up to that of Concorde (for what it's worth it's a pretty old plane). Much of this lead to its demise. Along with that, the down turn in air travel after 2001 lead to a big passenger slump which did not help keep the very expensive and rapidly aging plane in the air.
On an interesting (and similar side note) check out the Boeing SST which was a similar plane that never made it to production for similar reasons.