It was only the second time Everton have won in the Premier League after being two goals down following on from their comeback win over AFC Wimbledon in 1994.
The Toffees remain unbeaten on their travels this season, winning twice and drawing twice in the league while defeating both lower tier sides Barnsley and Reading in the League Cup.
"The reaction was the most pleasing aspect of the performance. We took responsibility and wanted to get a win with a completely different attitude," Martinez told reporters.
"Our first-half performance wasn't up to our normal level. We couldn't find passes and we were quite loose.
"In the second half, I wouldn't say it was a change from one or two players -- it was the whole team. We had a reset and then it was a completely different approach," the former Swansea manager added.
West Brom manager Tony Pulis said the Baggies were hurt by the loss of defenders Gareth McAuley, who was ruled out of the match, and Jonas Olsson, who was forced off due to a groin injury during the match.
"I don't think it helped that we lost McAuley yesterday and then lost Olsson after 15 minutes, and they are two players that when crosses come in they defend them very well, and Everton have scored off two crosses," Pulis told reporters.
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by Ian Ransom)
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