Atletico moved to the top of La Liga with their victory ahead of the clash between Real Madrid and Barcelona, which came courtesy of goals from Gabi and Diego Costa after the break.
Betis battled hard but never recovered from Braian Rodriguez's red card, given for a second bookable offence with 34 minutes to play.
Simeone said afterwards: "(I am) happy with the result.
"In the first half we struggled a bit, we played the second much better. Gradually we were getting into the game and taking it to the place we wanted.
"Gabi's goal came and that gave us tranquillity. (It) became much more difficult for Betis and we took advantage of that situation to win a very important match for us."
Gabi's goal – a 25-yard screamer that crashed into the bottom right corner – was worthy of winning any game.
And the 30-year-old gave credit to Betis for their battling display, which he says belied their position at the bottom of the table.
"We knew Betis plays very (well at home)…they are a decent team," Gabi said.
"In the end we got a fair victory. We have done what we had to do.
"Whatever the outcome (in Madrid, this win) will be good for us (in the title race)."
While Betis remain nine points adrift of safety, Atletico's push for their first La Liga title since 1996 continues to gather pace.
Simeone's side are next in action when they host Granada on Wednesday.
