Short-packet communications are applied to various scenarios where transmission covertness and reliability are crucial due to the open wireless medium and finite blocklength. Although intelligent reflection surface (IRS) has been widely utilized to enhance transmission covertness and reliability, the question of how many reflection elements at IRS are required remains unanswered, which is vital to system design and practical deployment. The inherent strong coupling exists between the transmission covertness and reliability by IRS, leading to the question of intractability. To address this issue, the detection error probability at the warder and its approximation are derived first to reveal the relation between covertness performance and the number of reflection elements. Besides, to evaluate the reliability performance of the system, the decoding error probability at the receiver is also derived. Subsequently, the asymptotic reliability performance in high covertness regimes is investigated, which provides theoretical predictions about the number of reflection elements at IRS required to achieve a decoding error probability close to 0 with given covertness requirements. Furthermore, Monte-Carlo simulations verify the accuracy of the derived results for detection (decoding) error probabilities and the validity of the theoretical predictions for reflection elements. Moreover, results show that more reflection elements are required to achieve high reliability with tighter covertness requirements, longer blocklength and higher transmission rates.