Try this:
Set a QLabel iside QPushButton rather than simple text. Then apply shadow effect to the label.
You may need to add extra code for centering the label inside the pushbutton.
mStartButton->setText("");
QLabel *label = new QLabel(mStartButton);
label->setText("<b>Button</b>");
QGraphicsDropShadowEffect* effect = new QGraphicsDropShadowEffect( );
effect->setBlurRadius( 5 );
label ->setGraphicsEffect( effect );