An own goal from Jose Gimenez on five minutes was enough for Betis to earn the points on Sunday.
Pellegrini later said: "The fact that they were the opponents and the few mistakes we made made, it was not only the best first-half of the season, but also the best game I have seen from the team since I arrived.
"It was the best game of the season, very complete. It's not easy to create so many chances for Atleti. It's not easy to play against them, who have had a very defined style for ten year."
He also said: "I'm very happy with the three points that allow us to stay in the European positions in the table, but I'm even happier with the team's performance. The first half was extraordinary in every sense.
"We deserved the win and to secure it with the chances we wasted, but this gave us a plus defensively. We are very secure in defence, and not by putting more players back, but by circulating and pressing in the opponent's half."
On a more direct Betis, the Chilean also said: "We had to change our system. We don't have Isco, Lo Celso, William, Rodri or Nabil, the kind of creative players who generate a lot of offensive volume, but we had five or six powerful forwards who are strikers and have other characteristics.
"We had to adapt to that. It was important to find another formula with those kinds of players instead of complaining about those who aren't there. We pressed very well in short distances. We didn't want to look for them up front because they had lost the ball when they left in recent games. It was the key to creating such a high offensive volume."