Recent advances in Deep Learning (DL) have improved multivariate time series (MTS) classification and regression by capturing complex patterns, but their lack of transparency hinders decision-making. Explainable AI (XAI) methods offer partial insights, yet often fall short of conveying the full decision space. Counterfactual Explanations (CE) provide a promising alternative, but current approaches typically prioritize either accuracy or sparsity -- rarely both -- limiting their practical value. To address this, we propose CONFETTI, a novel multi-objective CE method for MTS. CONFETTI uses Class Activation Maps (CAMs) to identify key subsequences, locates a counterfactual target, and optimally modifies the time series to balance prediction confidence and sparsity. This method provides actionable insights with minimal changes, improving interpretability, and decision support. CONFETTI is evaluated on seven MTS datasets from the UEA archive, demonstrating its effectiveness in various domains. CONFETTI consistently outperforms state-of-the-art CE methods in its optimization objectives, and in six other metrics from the literature, achieving, for example, at least 10% higher confidence while improving sparsity in at least 40%.