The Argentine watched his side maintain their perfect home record in Europe this season with a stoppage-time winner. Simeone celebrated fiercely on the touchline as Jose Maria Gimenez headed in Antoine Griezmann's 94th-minute corner to secure a vital victory.
"We played against an incredibly strong team, I think one of the best in the Champions League," Simeone said. "We knew that their pace and physicality could hurt us, so the first half was about limiting their football and running at them when we recovered the ball.
"We felt they would suffer on counter-attacks, especially if we got behind their wing-backs."
Atletico's opener arrived in controversial fashion when Alex Baena appeared to handle before Julian Alvarez scored from close range, but the goal stood after a VAR check. Inter responded through Piotr Zielinski, who struck a precise finish to level the match, but the visitors could not prevent Atleti from producing yet another decisive late moment at the Metropolitano.
Simeone said his side expected the dynamic of the match to shift after the break and credited his substitutes for sustaining the momentum. "We knew we could rely on another part of our repertoire in the second half," he said.
"The changes allowed us to continue the plan. Inter then tried to hurt us on transitions, but we kept pushing and fortunately took home a result we really needed."
Simeone admitted his wild celebrations reflected his nature rather than the circumstances. "I don't have comfort zones and I don't want them," he said. "We need to work with faith, love and quality.
"I have players who support me, and even the ones who did not start did what they needed to do."
Inter have now suffered five defeats in all competitions this season, but this was their first setback in the Champions League after they had arrived in Madrid with a perfect record. Atletico, meanwhile, remain flawless at home in Europe and strengthened their position in a fiercely competitive group.