Lukaku, a 28 million-pound ($40.9 million) signing from Chelsea in 2014, has been in excellent form this season and his second-half header at Goodison Park gave Everton a 2-1 win in the League Cup semi-final first leg.
"The stats are there to back any assessment of Lukaku, from our point of view he has always been the perfect striker for our football club," Martinez told Sky Sports.
"He is a young boy, he wants to be the best in the world."
Lukaku's physicality proved a constant menace for the City defence, who were on the back foot for much of the game.
Everton, who have never won the League Cup, restricted City to infrequent counter-attacks and Lukaku's presence ensured City's back four did not get a moment's peace all evening.
The Belgian forward found space between City's centre backs on 78 minutes to head home Gareth Barry's superb left-wing cross, just moments after the wind had been taken out of Everton's sails by Jesus Navas's equaliser.
The hosts had opened the scoring in first-half stoppage time when Ramiro Funes Mori had fired home after City keeper Willy Caballero could only parry Ross Barkley's firm shot.
City manager Manuel Pellegrini, however, complained that Lukaku was standing offside and in the visiting keeper's line of sight when Barkley's shot was struck.
"He is offside for the goal," Pellegrini said.
"(It is) Unbelievable the referee or linesman did not give offside."
(Reporting by Toby Davis; editing by Ed Osmond)
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