Everton were leading courtesy of Aaron Lennon's first-half effort when Seamus Coleman was punished by Oliver for handball, Jonjo Shelvey converting the resulting spot-kick.
Martinez, however, has questioned the decision, which came about when Coleman went to ground in the area under pressure from Marvin Emnes and touched the ball with his hand.
The former Swansea boss told BT Sport: "There is contact, he [Coleman] gets unbalanced.
"It's an action that's not a goal scoring threat, it needs common sense, is that handball? For me the whole action is too soft, I expect the referee to use common sense, there is not enough goal scoring threat to give a penalty.
"His [Coleman] feeling is that there is contact, he expects a free-kick, we felt the crowd were asking for it and unfortunately we were on the receiving end."
Martinez feels Shelvey's 69th-minute penalty denied his side a fourth straight Premier League win.
He added: "The result is hard to take.
"It feels like defeat, like we have dropped two points. We were so disciplined, and defensively we were perfect.
"We scored a very good goal from open play, my only criticism is that when we were too comfortable we didn't get the second goal. Apart from that I do feel the draw doesn't represent what happened on the pitch.
"It was one of most comfortable performances we have had away from home. We needed to score that second goal, we were so dominant, but good possession should end up with shot or more threatening positions."
The point edged Everton closer to securing top-flight safety with six games left.
"At this part of the season, every game is significant," said the Everton boss.
"We are building a winning mentality, we have learnt harsh lessons this season and every position in the league is important."
