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 on avoiding a fifth successive loss.
"At the moment the cup is such an important competition for us it would have been a 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.
"Rom at his best will change games
We carry a different threat.
"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."
West Ham manager Sam Allardyce could only bemoan Lukaku's knack of scoring against them.
"That man scores against us
Every time he plays against us he does," he said.
"The disappointing thing was we didn't make it two when we had the chance.
"Enner Valencia's (header saved by Joel Robles), particularly, we should have scored
That would have made it 2-0 and it would have made it too much for Everton to come back."
West Ham were missing injured striker Andy Carroll but Allardyce said it was not serious.
"He kicked the floor in training and bruised his foot but he will be fit and well for Saturday," he added.
Source : PA
Source: PA