The KC Chiefs fan who tackled an armed suspect at the parade shooting says he didn't think twice about going after him ... and the guy apparently had a big gun on him.

Paul Contreras is the person on video tackling one of the people who got detained Wednesday -- and he joined us on "TMZ Live" Thursday to tell us how he ended up being hailed a hero.

It all happened super fast ... Paul says folks were yelling at the crowd to tackle an individual who was running the opposite direction of everyone else. He had an angle on the guy and he says his instincts kicked in and he went out and pounced.

Paul tells us he was wrestling the man to the ground when he noticed a large firearm hit the deck. As others fled for their lives, Paul says he fought for his ... wrestling with the guy and trying like hell to keep him pinned until police came and eventually handled the rest.

Cops say there are at least 3 people in custody in connection with the deadly mass shooting -- but none of them have been arrested or booked on any charges as far as we know.

Paul, a Chiefs fan from Nebraska, was at the Super Bowl victory parade with his 3 daughters ... one of whom tells us she helped keep the gun away from the shooter once the weapon was on the ground. That seems to be who we see pick up the gun in the now-viral clip.

Cops say the shooting does not appear to have been an act of terrorism ... instead, authorities believe it was a dispute between multiple parties that escalated.

Police say 23 people were shot and one person died.