While Friar Laurence does make some poor decisions, it's actually debatable that he is the one to blame for Romeo's and Juliet's deaths. In fact, Prince Escalus makes some excellent points absolving Friar Laurence of any guilt and laying all blame on Lords Capulet and Montague. We see Prince Escalus absolving the friar in the line, "We still have known thee for a holy man" (V.iii.281). We further see him laying all blame on Lords Capulet and Montague in the lines, "See what a source is laid upon your hate, / That heaven finds means to kill your joys with love!" (V.iii.303-04). Escalus rightly blames Capulet and Montague rather than the friar because had their hatred not existed, Friar Laurence never would have been placed in a position in which he had to make poor decisions. He never would have had to marry them in secret, and he never would have had to fake Juliet's death, which are both events that lead up to their deaths. However, if you truly do want to make the point that he is to blame, then all you have to do is analyze his poor decisions as evidence.
His first poor decision was to marry the couple. While it broke neither state nor religious law to marry the couple in secret, Friar Laurence had his hesitations, which he should have abided by. It was neither unlawful nor irreligious to marry the couple in secret because under the Catholic Church a girl could marry at the age of 12 without parental consent, while a boy could likewise marry at 14 (Catholic Encycolopedia: "Civil Marriage"). Friar Laurence agreed to the marriage because he saw it as an opportunity to unite the two families, which could end the feud. However, at the same time, he hesitated because he especially saw Romeo as being far too young to truly know what real love is, as seen in Friar Laurence's metaphor comparing Romeo's love to a young child who is too young to know how to read, "Thy love[for Rosaline] did read by rote[memory], and could not spell" (II.iii.91). Aside from expressing his view that Romeo is too young to know what real love is, we see Friar Laurence express his hesitation in his opening lines of Act 2, Scene 6, just before he marries them. He expresses his hesitation by hoping out loud that God will not later punish them for this holy act.
Aside from the decision to marry the couple, Friar Laurence's second poor decision was to fake Juliet's death. This plan went so foully awry that Romeo believed she was truly dead and killed himself so he could lie by her side, which led to Juliet's own real death as well. Faking Juliet's death was a very impetuous, unnecessary action. Juliet's father had already threatened to disown her should she refuse to marry Paris; therefore, what more could she gain to lose if Friar Laurence simply intervened on her behalf, explained his involvement in the couple's secret marriage, and then brought her to Romeo in Mantua? Had Friar Laurence taken the more honest route, the end result would have been the same--she would have been united with exiled Romeo in Mantua, which would have spared the couple's death. However, again, Friar Laurence would have never have had to decide to marry them in secret nor to fake Juliet's death had the hatred between the Capulets and Montagues not existed; therefore, it is really Lords Capulet and Montague who are to blame for their children's deaths, as well as all the deaths in the play.