Everton battled valiantly and had their chances against the visitors, with Romelu Lukaku hitting the crossbar using a first-half free-kick.
Nevertheless, City turned around the style soon after the break and secured victory through targets from Aleksandar Kolarov and Samir Nasri, leaving Martinez to rue what could happen to be.
Speaking to BBC Sport, he said: “It’s somewhat bit hard to take due to the fact I feel we had extremely good moments.
“If we could get the first aim it would have changed the game. Overall I felt we didn’t have that bit of luck you need in the six-yard box.
“We had the very best moments inside the first half and carried a true threat. The first goal was a real negative moment for us. We had been sloppy.”
With just per week remaining on the transfer window, the Spaniard who played fifa 16 coins expects to be busy adding to his squad, with River Plate defender Ramiro Funes Mori inside the stands at Goodison Park having been linked all through the summer.
On the 24-year-old central defender, Martinez said: “It’s not carried out. He’s right here, we have to meet over the next 24 hours and see if we can conclude a deal with his club.
“I count on a couple of signings inside the subsequent couple of days,” he added.
Everton suffered a blow just just before half-time, with Brendan Galloway suffering an injury before getting substituted for Tyias Browning.
Martinez revealed that Galloway was sidelined with “a patella tendon problem”, and will be assessed more than the coming days.