Although there have been remarkable advances in dialogue systems through the dialogue systems technology competition (DSTC), it remains one of the key challenges to building a robust task-oriented dialogue system with a speech interface. Most of the progress has been made for text-based dialogue systems since there are abundant datasets with written cor- pora while those with spoken dialogues are very scarce. However, as can be seen from voice assistant systems such as Siri and Alexa, it is of practical importance to transfer the success to spoken dialogues. In this paper, we describe our engineering effort in building a highly successful model that participated in the speech-aware dialogue systems technology challenge track in DSTC11. Our model consists of three major modules: (1) automatic speech recognition error correction to bridge the gap between the spoken and the text utterances, (2) text-based dialogue system (D3ST) for estimating the slots and values using slot descriptions, and (3) post-processing for recovering the error of the estimated slot value. Our experiments show that it is important to use an explicit automatic speech recognition error correction module, post-processing, and data augmentation to adapt a text-based dialogue state tracker for spoken dialogue corpora.