That "pull" that you're feeling is the torque. It has amazing low-end torque. Horse power is a RPM thing and best used for land speed records. Torque is what moves the car from a dead stop and what accelerates us out of the corners.
Simply put, horse power is torque times RPM. hp = T * RPM
That's why a spec sheet always has HP ratings at RPM numbers like 6500. There isn't enough HP at 3,000 RPM to power a flash-lite.
Sorry, but that is incorrect. If it was correct you could remove the engine and replace it with a big ape and a torque wrench and have a car that would have great performance. The fact is that power applied to the clutch is what you need to accelerate. To accelerate hard consistently you need the engines power band to be wider than the steps between gears. This is why more gears yields better acceleration (assuming fast gear changes) and why cars with CVTs accelerate better for a given amount of power to weight ratio.
A car is perceived as "punchy" if it can produce a lot of power at a typical running gear. This can be done by having a wide power band, or by messing with the gears. For example, my 1971 Norton Commando was "punchy", but achieved that by having low gears rather than by having a wide power band. A wide power band by definition requires a lot of torque relative to the RPM range of the engine, so we get this tendency to associate more torque with better acceleration. However, it is the amount of available power that matters in all cases.