The Red Devils were eager to bounce back after being held to a 2-2 draw by Stoke last time out in the Premier League and Sunday's performance at Old Trafford didn't disappoint.
United opened the scoring just four minutes into the clash with Antonio Valencia breaking the deadlock but they failed to convert further chances in the opening 45 minutes.
However, Henrikh Mkhitaryan, Lukaku and Anthony Martial wrapped up the three points to complete a 4-0 triumph in the last 10 minutes.
The Belgian felt the result should have been sealed much earlier against his former club but praised United for eventually showing their real quality.
"We could have scored more in the first half. We weren't clinical enough. Everton created problems in midfield and the manager gave us tips at half-time of how to sort it," Lukaku told Sky Sports.
"In the second half, Everton had a lot of control but quality was the difference in the end."