The Toffees survived two penalties and were on the back foot for the vast majority of the match, but still managed to come away from the Etihad Stadium with a 1-1 draw.
Lukaku opened the scoring for Ronald Koeman's side and expressed disappointment at not holding out for an unlikely win, but acknowledged that a draw is still a good result.
"We have to be happy with a point. City were good, they have top-quality players," he told reporters.
"When you are under pressure like that against the best team in the league at the moment you have to be strong mentally and defend well, be as a team. We had to encourage each other and be positive.
"When we came up with the lead I thought if we had got the second it would have been a totally different game. But you have to be focused and we lacked a bit of focus when they scored, but we defended well for the rest of the game."
Lukaku has now scored six goals in his last five Premier League appearances.