The Blues had to fight back after going 1-0 down late on at Goodison Park.
The Blues dominated proceedings at Goodison Park on Monday evening, hitting the woodwork three times, and Tom Cleverley was denied by a wonder save from Palace 'keeper Wayne Hennessey.
They found themselves 1-0 down late on though, with defender Scott Dann heading home from a corner to stun the home crowd.
The Blues fought back as Lukaku turned in a Gerard Deulofeu cross, and he says the fight back shows the great character in the team this season.
“We had a lot of chances and we were unlucky when we hit the crossbar,” he told Sky Sports.
“After their goal we reacted well, it shows we have great character in the team."
The goal was Lukaku’s 50th in 100 appearances for the Blues, an impressive record for a player who is yet to reach his 23rd birthday.
He has been in fine form for them this season, with 14 goals in all competitions so far this season, with 11 of those coming in the Premier League.
That would put him top of the charts if it weren’t for the remarkable performances of Leicester City’s Jamie Vardy this season.
He though was insistent on focusing on the team and not personal accolades despite his impressive feat.
"I am proud but I'm a team performer, so I'm happy with the record but disappointed we didn't get the three points,” he added.