In practice, yes, chemical rockets are very limited in what they can achieve, because they consume fuel to accelerate, and by bringing more fuel they grow in weight, yielding diminishing returns from each additional kilogram of fuel. The Tsiolkovsky rocket equation describes exactly how that works.
With chemical propulsion, we can do one way trips to the edge of our solar system in about 30-40 years (the Voyagers are there now; New Horizons will be, before very long). The nearest stars are about 1000 times further away than that, and we don't have any practical way of building a machine that can last for 30,000 years.
For the next phases of exploration of our own solar system, various electrical rocket propulsion technologies are attractive; their exhaust velocities are much higher than those of chemical rockets, so for the same mass of propellant they can achieve much higher speeds. That still requires thousands of years for interstellar travel.