Massive star-forming regions are thought to be the most common birth environments in the Galaxy and the only birth places of very massive stars. Their presence in the stellar cluster alters the conditions within the cluster impacting at the same time the evolution of other cluster members. In principle, copious amounts of ultraviolet radiation produced by massive stars can remove material from outer parts of the protoplanetary disks around low- and intermediate-mass stars in the process of external photoevaporation, effectively reducing the planet-formation capabilities of those disks. Here, we present deep VLT/MUSE observations of low-mass stars in Trumpler 14, one of the most massive, young, and compact clusters in the Carina Nebula Complex. We provide spectral and stellar properties of 717 sources and based on the distribution of stellar ages derive the cluster age of ~1Myr. The majority of the stars in our sample have masses <=1M_{sun}_, what makes our spectroscopic catalogue the most deep to date in term of masses, and proves that detailed investigations of low-mass stars are possible in the massive but distant regions. Spectroscopic studies of low-mass members of the whole Carina Nebula Complex are missing. Our work provides an important step forward towards filling this gap and set the stage for follow-up investigation of accretion properties in Trumpler 14.