Tybalt is, of course, partially to blame for the deaths of Romeo and Juliet; however, he is not ultimately to blame. We must remember that, while Tybalt has his own character flaws such as a hot, fiery temper, Tybalt was only acting in response to a longstanding tradition, a longstanding tradition of hatred and feuding.
We learn from the Prologue just how long the family feud between the Montagues and Capulets has been going on. We learn that the two families have had an "ancient grudge," meaning dating far, far back to a "remote period," generations and generations ago (Prologue.3, Random House dictionary). Not only is their grudge "ancient," the grudge had been buried for a while but this generation of Capulets and Montagues have decided to stir up the fight again. Hence, the unfounded hatred that Tybalt feels for Romeo is not necessarily Tybalt's fault because it stems from an ancient tradition plus from his uncle's own decisions and influence. Had Tybalt not been influenced to hate all Montagues, Tybalt never would never have felt insulted by Romeo's presence at their ball and never would have challenged Romeo to a duel. Therefore, by the end of the play, Prince Escalus is correct in blaming both Lords Capulet and Montague for all of the deaths in the play.
However, while Tybalt's actions were influenced by Lord Capulet's actions, making Lord Capulet more to blame than Tybalt, Tybalt is not completely blameless. Tybalt has some character flaws that drove him to make the choice to challenge Romeo. Namely, Tybalt has a hot, fiery temper and is very quick to judge situations by using his temper rather than his rational mind. We see evidence of Tybalt's irrational, fiery temper in the very first scene. When Tybalt sees Benvolio with his sword drawn amongst Capulet and Montague servants, Tybalt is very quick to assume that Benvolio started the fight, as we see from his lines addressed to Benvolio, "What, art thou drawn among these heartless hinds? / Turn thee, Benvolio! look upon thy death" (I.i.61-62). The word hinds(it) literally means "hounds," but can be translated as referring to "stupid servants" (eNotes). Tybalt feels shocked that a man of Benvolio's station would pick a fight with lowly servants and charges to challenge Benvolio. However, the reality is that Benvolio was actually trying to break up the servants' fight, showing us just how poorly Tybalt used his temper to judge the situation. He even poorly judges Romeo's reasons for being present at the ball and assumes Romeo is there to mock their ball. All of this shows that Tybalt makes poor, irrational, emotionally charged decisions and this character flaw is also to blame for not only Romeo's death but his own death as well.