The hosts were denied a first Merseyside derby win since October 2010 thanks to Daniel Sturridge's header from a Steven Gerrard free-kick a minute from time at Goodison Park.
Liverpool had previously taken the lead twice, first through Philippe Coutinho following a knockdown from a corner after five minutes and then courtesy of a brilliant Luis Suarez free-kick - and Martinez was unhappy at how his side conceded in the game.
"The two teams played in the right manner, created a lot of chances," he told BT Sport.
"But conceding two goals from set pieces is very disappointing. We were (trailing twice) when Liverpool didn't even have a shot on target (from open play).
"Overall I think we had the better chances, I think Liverpool got too big a reward from the game. But overall it was a fantastic football game."
Romelu Lukaku scored his sixth and seventh Premier League goals of the season in the 72nd and 82nd minutes as Everton looked to be on their way to a long-awaited victory over their local rivals.
And even though Sturridge had the final say in the dying minutes, Lukaku remains confident about Everton's chances of success this season.
"To play in the derby was such an honour and two score two goals. My team-mates helped me a lot. To help the team get back in the game, it was great. The pity was that we didn't win," he said.
"It was a great header. We worked a lot of set pieces, but it usually doesn’t come off. Week after week I just try to improve. Every game in the Premier League is a big challenge.
"This year we have a great squad, a lot of experience and a lot of young players too. It's a good mix. Hopefully we’ll end up very high in the league. Champions League - why not?"
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