City's Raheem Sterling played in Aleksander Kolarov for the opener and the left-back beat Tim Howard at his near post after the Everton goalkeeper dived the wrong way in the Premier League contest.
“I think the first goal seemed to be too important today,” Martinez said.
“We always knew it was going to be an important one playing against a quality side, but I think it affected us a little bit too much,” the manager added.
“It comes from us being very sloppy on the ball and us giving them a counter-attack, which ended up in the back of our net and that gave them a real sense of control,” the Spaniard said.
“I thought up to that goal, especially in the first half, we probably had the best moments in the game.
“We defended really well ... but we didn't have our normal composure or the know-how that we usually carry,” Martinez added.
“In terms of effort and the way in which we had a proper face-to-face confrontation with a team, who, in my eyes, are the best in the league at the moment ... we can take a lot of positives from that,” the 42-year-old said.
The manager also confirmed that left-back Brendan Galloway was withdrawn during the first half due to a knee injury and that Costa Rican Bryan Oviedo was ready to return for the first time since April after breaking a bone in his right foot.
“Brendan has been terrific and we as a football club are ready to give young players an opportunity,” Martinez told the club website (www.evertonfc.com).
“He picked up a patella tendon problem that we'll assess in the next 24 to 48 hours. It's probably more to do with his age and the fact he's still growing rather than a structural injury.
“Bryan Oviedo is fully fit and needs a bit of match fitness now. Hopefully we'll see him on the pitch very soon,” Martinez added. – Reuters
Original source: Everton lacked ‘know-how’ - Martinez