I have a series of $n$ independent random variables $X_1,\ldots, X_n$, each with the support $[0,1]$, and a monotone convex function $f:\mathbb{R}^n \rightarrow \mathbb{R}$ that is 1-Lipshitz in L1 norm, i.e., for every $x,y \in \mathbb{R}^n$, it holds that $f(x)-f(y) \leq \sum_{i=1}^{n} |x_i-y_i|$. I want to have a concentration bound like Talagrand.

Is it true that $$Pr[ \mid f(X_1,\ldots,X_n) - E[f(X_1,\ldots,X_n)] \mid > t] \leq c_1 \cdot e^{-\frac{t^2}{c_2}} $$ for some constants $c_1,c_2>0$ (that are independent of $n$, and the distributions of $X_i$, and the function $f$, as long as the conditions hold)?

Do I need more conditions for the inequality to hold?