In modern online platforms, incentive (\textit{e.g}., discounts, bonus) are essential factors that enhance user engagement and increase platform revenue. Over recent years, uplift modeling has been introduced as a strategic approach to assign incentive to individual customers. Especially, in many real-world applications, online platforms can only incentivize customers with specific budget constraints. This problem can be reformulated as the multi-choice knapsack problem (MCKP). The objective of this optimization is to select the optimal incentive for each customer in order to maximize the return-on-investment (ROI). Recent works in this field frequently tackle the problem of budget allocation using a two-stage approach. %: the first stage utilizes causal inference algorithms to estimate the individual treatment effect or uplift, while the second stage employs integer programming techniques to determine the optimal solution for budget allocation. However, this solution is confronted with the following challenges: (1) The commonly used causal inference methods often ignore the domain knowledge in online marketing, where the expected response curve of a customer should be monotonic and smooth as the incentive increases. (2) There is an optimality gap between the two stages, resulting in inferior sub-optimal allocation performance, which is due to the loss of the incentive recommendation information for the uplift prediction under the limited budget constraint. To address these challenges, we propose a novel \underline{E}nd-to-\underline{E}nd Cost-\underline{E}ffective \underline{I}ncentive \underline{R}ecommendation (E$^3$IR) model under the budget constraint. Specifically, our methods consist of two modules: the uplift prediction module and the differentiable allocation module. In the uplift prediction module, we construct prediction heads to capture the incremental improvement between adjacent treatments with the marketing domain constraints (\textit{i.e.}, monotonic and smooth). %To obtain a monotonic user response curve, we constrain the output of each prediction head to be non-negative. In the differentiable allocation module, we incorporate integer linear programming (ILP) as a differentiable layer input. Furthermore, we conduct extensive experiments on both public and real product datasets, which demonstrate that our E$^3$IR improves allocation performance compared to existing two-stage approaches.