This study proposes a new deep learning-based method that demonstrates high performance in detecting Covid-19 disease from cough, breath, and voice signals. This impressive method, named CovidCoughNet, consists of a deep feature extraction network (InceptionFireNet) and a prediction network (DeepConvNet). The InceptionFireNet architecture, based on Inception and Fire modules, was designed to extract important feature maps. The DeepConvNet architecture, which is made up of convolutional neural network blocks, was developed to predict the feature vectors obtained from the InceptionFireNet architecture. The COUGHVID dataset containing cough data and the Coswara dataset containing cough, breath, and voice signals were used as the data sets. The pitch-shifting technique was used to data augmentation the signal data, which significantly contributed to improving performance. Additionally, Chroma features (CF), Root mean square energy (RMSE), Spectral centroid (SC), Spectral bandwidth (SB), Spectral rolloff (SR), Zero crossing rate (ZCR), and Mel frequency cepstral coefficients (MFCC) feature extraction techniques were used to extract important features from voice signals. Experimental studies have shown that using the pitch-shifting technique improved performance by around 3% compared to raw signals. When the proposed model was used with the COUGHVID dataset (Healthy, Covid-19, and Symptomatic), a high performance of 99.19% accuracy, 0.99 precision, 0.98 recall, 0.98 F1-Score, 97.77% specificity, and 98.44% AUC was achieved. Similarly, when the voice data in the Coswara dataset was used, higher performance was achieved compared to the cough and breath studies, with 99.63% accuracy, 100% precision, 0.99 recall, 0.99 F1-Score, 99.24% specificity, and 99.24% AUC. Moreover, when compared with current studies in the literature, the proposed model was observed to exhibit highly successful performance. The codes and details of the experimental studies can be accessed from the relevant Github page: (https://github.com/GaffariCelik/CovidCoughNet).