In Act III, scene II, Juliet is confused by the Nurse and her sobbing. At first she thinks that Romeo is dead. The Nurse does nothing to correct her at first. Then the Nurse says Tybalt's name. So because of all the confusion in this scene between the Nurse and Juliet, Juliet is not truly able to grieve properly for her cousin. She is upset that he's dead, but she has mixed emotions going back and forth about how she feels about Romeo. How could he do this?
"O serpent heart, hid with a flowering face!
Did ever dragon keep so fair a cave?
Beautiful tyrant! fiend angelical!
Dove-feather'd raven! wolvish-ravening lamb!
Despised substance of divinest show!
Just opposite to what thou justly seem'st,
A damned saint, an honourable villain!"
He appears angelic, yet he murdered her own blood. She's confused. So she is not able to fully grieve for Tybalt. She's more worried about how that affects Romeo and if they can still be together. She does use her so-called grief over Tybalt's death to avoid a lengthy conversation with Paris.
At first she is upset and angry because her husband killed her cousin, but after she realizes that if Romeo didn't kill Tybalt he would have killed Romeo. She then sides with Romeo to be loyal and after that we don't hear anything about her feelings for Tybalt. Most likely she doesn't care much after.
However, in Act 4 - Scene 5 when she is talking about being in the tomb with Tybalt's dead body she mentions at the end of her soliloquy how his ghost will try and get revenge on her. Maybe she feels guilty here?