The Belgium striker converted Bryan Oviedo’s cross to cancel out James Collins’ 56th-minute header to keep the Toffees in the FA Cup.
It also halted a run of four successive defeats which looked like turning into their worst sequence since 2005.
“It would have been very damaging but you always get an opportunity to win the next game,” said Martinez.
“At the moment the cup is such an important competition for us it would have been an horrendous setback.
“It is very important we are still in the cup and now look forward to the next game in the league (at home to Manchester City) but still aware we are in a bad run.”
Lukaku’s goal, his fourth in as many appearances against West Ham, may have only secured a replay but it felt much more significant than that.
Asked about the importance of the goal, Martinez added: “Huge. When you walk into a dressing room with a defeat it is a completely different situation.
“It is a big moment to be able to go in with different emotions and I am extremely proud of the players.”
Martinez also praised Lukaku on his return to the starting line-up after two games on the bench.
“The whole week he has trained very well and his attitude was perfect,” he said.
“Romelu at his best will change games. We carry a different threat (with him). I was really pleased with his attitude, showing real responsibility and maturity.
“In a period like ours you have two options, you can shy away and hide or you can take responsibility.”