How to add events in saved block

I have this component

class CallToAction extends Component {
	handleChange() {
		console.log('changed');
	}

  render() {
    return (
      <input type="text"
				value={ this.props.cta }
				onChange={ this.handleChange }/>
    );
  }
}

When I include it in the edit: method of my block, the onChange fires and logs ‘changed’ as expected

When I include it in the save: method of my block, it does not work.