Passive acoustic monitoring can be an effective way of monitoring wildlife populations that are acoustically active but difficult to survey visually. Digital recorders allow surveyors to gather large volumes of data at low cost, but identifying target species vocalisations in these data is non-trivial. Machine learning (ML) methods are often used to do the identification. They can process large volumes of data quickly, but they do not detect all vocalisations and they do generate some false positives (vocalisations that are not from the target species). Existing wildlife abundance survey methods have been designed specifically to deal with the first of these mistakes, but current methods of dealing with false positives are not well-developed. They do not take account of features of individual vocalisations, some of which are more likely to be false positives than others. We propose three methods for acoustic spatial capture-recapture inference that integrate individual-level measures of confidence from ML vocalisation identification into the likelihood and hence integrate ML uncertainty into inference. The methods include a mixture model in which species identity is a latent variable. We test the methods by simulation and find that in a scenario based on acoustic data from Hainan gibbons, in which ignoring false positives results in 17% positive bias, our methods give negligible bias and coverage probabilities that are close to the nominal 95% level.