Lukaku scored twice in their 3-0 defeat of Genoa.
"On a personal level, I am happy, but I also say that as a team we can do so much more," the Belgian told Sky Sport Italia.
“We have a good squad, it's not easy for us to be in second place, because we want to win and go as high as possible. I want to help Inter achieve that.
“We dropped too many points along the way, but we are young and eager to improve. Now we want to do well in these final rounds and then the Europa League."