Antonio Conte's title ambitions took a knock with back-to-back stalemates against Roma and Fiorentina.
But Inter pulled back ahead of Atalanta, and within four points of leaders Juventus, who are poised to claim a 36th 'Scudetto' when they play Sampdoria in Turin.
"The problem is how you see the glass, whether half full or half empty," said Conte of second position.
"There are vintages where you sow little and you reap a lot and others in which you sow a lot and reap little, like this one.
"But there are numbers that speak clearly, that comfort. I think these lads are doing very good things. Of course, we can and must improve.
"We won't win the league but we have to be hungry to finish as high as possible."
Lukaku nodded in Cristiano Biraghi's cross after 34 minutes in the northwestern port city, with the former Manchester United forward accelerating to finish off an individual effort three minutes into injury time.
The 27-year-old Belgian brought his tally to 23 league goals this season, and 29 in all competitions.
Alexis Sanchez, on-loan from United, was also on target with eight minutes to go, picking up a Victor Moses cross to volley in for his fourth league goal this season.
Atalanta were held 1-1 at AC Milan on Friday, with the Bergamo side due to meet Inter Milan in the final game of the season next week.
"On a personal level, I'm happy, but as a team we can do so much more," said Lukaku, who moved third behind Hungarian Istvan Nyers (26) and Brazilian Ronaldo (25) for the mosts league goals scored by an Inter player in their debut season.
"It's not easy for us to be in second place, because we want to win and go as high as possible.
"Now we want to do well in these final rounds and then the Europa League."
– Four Sassuolo goals offside –
Genoa are four points above the relegation zone with two games left this season.
In Naples, Napoli beat Sassuolo 2-0 with the visitors having four goals ruled offside — two in either half.
Three were chalked off by VAR.
Albanian defender Elseid Hysaj opened the scoring for Napoli after eight minutes in the San Paolo Stadium.
Filip Djuricic then had two goals ruled out as did Francesco Caputo and Domenico Berardi following VAR viewings before Brazilian Allan sealed the points for the hosts three minutes into injury time.
Seventh-placed Napoli — already through to the Europa League as a result of their Italian Cup victory — extend their lead on pursuing Sassuolo, in eighth, to 11 points.
Mid-table Parma saw off relegated Brescia 2-1 in a win inspired by on-loan Juventus midfielder Dejan Kulusevski.
The 20-year-old Swede set up Matteo Darmian for the opener just before the hour mark before Daniele Dessena pulled the hosts level three minutes later.
A spectacular solo effort from Kulusevski sealed back-to-back wins for Parma who had struggled after the lockdown.