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City fell behind when Wayne Rooney scored after 34 minutes, before Kyle Walker was dismissed for two yellow cards just before the break.
Guardiola's men battled admirably after the restart despite the numerical disadvantage with substitutes Raheem Sterling, Danilo and Bernardo Silva all making an impact; most impressively via the England winger's volleyed equaliser after 82 minutes.
The Catalan boss said: "We are here for the results. We made absolutely everything to try and win with ten men against a good Everton team. I prefer to win the game, we were not able to. We want to start well at home. It’s just the second game and we’ll improve."
Commenting on the Sterling strike and the tactical changes he was forced into Guardiola added: "It was a good goal. Sterling was good and I think he is a guy who prefers playing in the middle rather than out wide. Bernardo and Danilo played well in the second half as well.
"We tried to win the game after half time even though we had 10 against 11. We changed to four at the back and put guys like Kevin and David in the middle to try and find chances. Fernandinho did amazing to help us, filling in at the back. Nobody can say we didn’t try but, of course, we are here to analyse the results and it wasn’t good enough.
"We created chances before the (Everton) goal. Williams, Jagielka, Keane and Baines are all very good in one versus one situations. We tried to find ways of attacking them and we did. Our amount of opportunities was up there all the time. We never gave up. It was like the spirit of Mancunians.
"Last season we were the first or second team creating the most clear chances. At this level, it’s about the result. They arrived once (in our box)."
On Bernardo Silva's eye-catching cameo Guardiola said: "I think good players can adapt everywhere and very quickly. He has goals and assists. He doesn’t lose the ball, which is very important to me."
City must quickly refocus for the trip to Bournemouth in Saturday's lunch-time kick-off.