Approximating joint smoothing distributions using particle-based methods is a well-known issue in statistical inference when operating on general state space hidden Markov models (HMM). In this paper we focus on non-asymptotic bounds for the error generated by the computation of smoothed additive functionals. More precisely, this contribution provides new results on the forward filtering backward smoothing (FFBS) Lq-mean errors under appropriate mixing conditions on the Markov kernel's probability density function. The algorithm used has a computational complexity depending linearly on TN where T is the number of observations and N the number of particles. The main improvement concerns the rate of convergence of these norms which depends on T and N only through the ratio T/N for additive functionals (i.e. with norm proportional to T). This paper relies mainly on recent exponential deviation inequalities on the smoothing error.