If T-Rex and its species never fed on smaller prey at once in their entire life, couldn't that be the reason why they've suddenly go extinct?

T-rex probably often if not mostly ate animals smaller than itself.  They didn't go extinct faster.  In fact, dinosaurs were having trouble at the end of the Cretaceous but T-rex survived right until the end.   

Trex was a 6-10 ton carnivore, it was very active, a hypercarnivore, so the amount of calories it needed is incomparable to any land animal today. 

After the meteorite struck there was a nuclear winter which lasted an estimated decade, phytoplankton and vegetation collapsed so you vet your *** nothing as large and active as trex survived. 

Even small herbivores died out so you could imagine. The only warm blooded animals to survive were tiny generalist [birds and mammals, rat sized], at the time pterosaurs were not very small [smallest was the size of a seagull], so they too were doomed. 

T. rex lived right up to the moment the giant meteor struck the earth 65 million years ago, and so did Triceratops. That is why both kinds of dinosaurs are so abundant as fossils. When they died, all other dinosaurs also became extinct. Their carcasses were largely untouched by scavenging dinosaurs, allowing them to be preserved. The meteor striking the earth created oven-like temperatures on the ground, instantly scorching the lungs of all animals that cannot find a cooler place to live. 100 percent of dinosaurs, 100% of the enantiornithine birds, and 100 percent of the pterosaurs were wiped out. The only reason we are around is because our ancestors were shrew-like animals that lived mostly underground. Since heat rises, temperature underground was safe for shrew-like mammals, lizards, snakes, toads, salamanders, and many invertebrates. Another safe place to be was the water, where crocodiles, turtles, newts, shorebirds, insects with aquatic larvae, fish, frogs, and the platypus lived. Water takes a long of energy to heat up. Since T. rex and all other dinosaurs were land animals and they were too big to live underground, they all vanished. Even marsupial mammals that were living above ground were wiped out. 

Uh, the reason they suddenly went extinct is because a big meteor hit the Earth.  The part of the world where they lived was set on fire.  It was a huge dinosaur roast.  Half of EVERYTHING living on Earth died WITHIN DAYS because of getting cooked.

It wasn't THAT sudden. And the main reason is more likely to be because their prey (mammals) ate their eggs before they hatched.