"I wanted to give my version after hearing so many things," Messi told Barcelona's club television. "I have never asked that they replace a coach, and I never would. This hurts. And it comes from people who want to hurt the club.
"I have heard many things, both before and now, that make it look like I run the club. I am a player. I don't take decisions and I don't want to."
As big as his performance was on the pitch, Messi's appearance on club television will likely do more to settle down the club's fans and relieve pressure on Luis Enrique.
The coach, however, didn't think even this big win would open a new chapter for the team.
"Without a doubt, wins are the only thing that can calm this wave," said Luis Enrique. "All wins reinforce the team, but these are three points, nothing more. When we lose again the tension will come back. It is inevitable."
Atletico, in third, fell four points behind Madrid, which has a game in hand.
Elsewhere, Sevilla tightened the race at the top with a 2-0 win at Almeria thanks to goals by Vicente Iborra and Jorge "Coke" Andujar, moving into fourth place two points behind Atletico.
Elche moved off last place with a 2-1 win at Athletic Bilbao in its first victorious visit to the Basque club after 20 trips.
Granada fell to the bottom of the standings after a 14th straight game without a win following its 1-1 draw at home with Real Sociedad.
Eight months ago Atletico won the title in a winner-takes-all finale at Camp Nou, whose fans ended up honoring the victors while jeering their own team.
On Sunday, it was "Messi! Messi!" that rang out after Suarez's goal.
Messi was awarded a trophy by the Spanish league before kickoff for breaking Telmo Zarra's all-time scoring record in November that had stood at 251 goals since 1955.
Messi then proceeded to wreak havoc from his spot on the right side of the attack with repeated dribbles into the thick of Atletico's area.
He unlocked the defense with a burst of speed before his short cross eventually fell to Neymar after Suarez couldn't control it for the Brazil striker to toe past goalkeeper Miguel Moya's reach.
With Barcelona pressing for a second goal, Atletico turned up its physicality with hard fouls on both Neymar and Messi. Neymar spent five minutes on the sideline having a bloody right ankle tended to after Jose Gimenez's tackle.
But Suarez got his second goal in 10 league matches after Messi sprinted with the ball at his feet for half the pitch and passed to the striker. Televised replays showed what the referee had missed: Messi used his arm to control the ball at the start of his run.
The referee didn't let Messi get away with a slight kick that grazed Jesus Gamez's boot to set up Atletico's goal.
Messi combined with Ivan Rakitic to get his goal from close.