Guns were around a long time before these types of killing sprees became an almost regular occurance.
People who choose to do such evil, be it from mental illness or just plain meanness, will kill people, with or without guns. Had he not been able to purchase a gun, he would've made a bomb, he'd have found a way. People who are intent on evil are intent on evil. He wouldn't have just said, "well, I want to kill some people, but I can't go legally by a gun, so I guess I'll scrap the whole thing."
There are many factors in these tragedies to consider - increased violence (movies, games, music, etc), mental illness, media sensationalism, cruelness of others while authorities ignore it, the breakdown of traditional families/values, physical/mental/sexual abuse - the lists go on, and no one can agree on where the root cause/blame lies.
To simply say that taking away legal means of purchasing guns would solve the issue is overly simplistic and unrealistic.