The Toffees struggled to match Spurs during the opening 45 minutes at Goodison Park, but they rallied after the break on their way to earning a share of the spoils.
"In the first half Spurs had the initiative in the game," Martinez told BBC Sport. "We were good defensively but we lost the ball too cheaply.
"In the second half we were completely different, imposed ourselves and forced Spurs to defend in their own half.
"It was a very level game but what I will take from it is our character. We found a way to impose ourselves in the second half and both teams tried to win until the last seconds."
Despite the draw, Everton remain in seventh place in the Premier League table after 10 matches.