The Merseyside club shared a 2-2 draw with Norwich City on the opening day, and were held to a 0-0 stalemate by West Brom at Goodison Park on Saturday.
But Martinez believes his team deserved more from both fixtures, and has argued that their performances bode well for the future.
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"I think in any draw you look at it and you think 'we got away with a point' or 'we were unfortunate not to get the three points'. I think at Norwich clearly with the amount of chances that we had and scoring the second goal before the home side it was a disappointment to drop the two points.
"Today, I thought the first half we got a little bit frustrated but as the game went on you could only see us scoring. Yes, West Brom have got a real good threat in set plays and we dealt with it really well, they were really well poised in the counterattack and I thought we coped with that really well.
"There are many areas we need to improve but keeping a clean sheet today in the manner that the game was is very encouraging and I see two positive draws rather than points dropped on both."
The Spaniard handed a second consecutive start to 19-year-old midfielder Ross Barkley for the visit of West Brom, and he has hailed the youngster’s early contributions.
"I've been very impressed with Ross. I think at his age it's incredible the manner that he has developed his game," Martinez added.
"Sometimes you see a youngster with enormous potential and enormous talent and somehow you need to use that. With Ross it's the opposite.
"He can fit in in different roles, he's a thinker, he makes fantastic decisions in where the space is. I've been very impressed so far and I know he's going to go from strength to strength, he's an incredible talent."