Standard optical tweezers rely on optical forces that arise when a focused laser beam interacts with a microscopic particle: scattering forces, which push the particle along the beam direction, and gradient forces, which attract it towards the high-intensity focal spot. Importantly, the incoming laser beam is not affected by the particle position because the particle is emph{outside} the laser cavity. Here, we demonstrate that emph{intracavity nonlinear feedback forces} emerge when the particle is placed emph{inside} the optical cavity, resulting in orders-of-magnitude higher confinement along the three axes per unit laser intensity on the sample. We present a toy model that intuitively explains how the microparticle position and the laser power become nonlinearly coupled: The loss of the laser cavity depends on the particle position due to scattering, so the laser intensity grows whenever the particle tries to escape. This scheme allows trapping at very low numerical apertures and reduces the laser intensity to which the particle is exposed by two orders of magnitude compared to a standard 3D optical tweezers. We experimentally realize this concept by optically trapping microscopic polystyrene and silica particles inside the ring cavity of a fiber laser. These results are highly relevant for many applications requiring manipulation of samples that are subject to photodamage, such as in biological systems and nanosciences.