The Exiles, who are a point outside the play-off places and host Tottenham in the FA Cup fourth round on Saturday, took a first-half lead courtesy of Ben Tozer.
But Morecambe captain Michael Rose levelled the scores with a penalty in the second half.
“I’m disappointed and I think it was two points dropped,” said Newport manager Michael Flynn.
“The manner in which we conceded a goal wasn’t good enough. I thought we were comfortable for the majority of the game.
“We’ve got to be more ruthless in the opposition penalty box. I don’t think the Spurs game affected the boys one bit because for the majority of the game we were the better team by far.
“We should have won this game but it’s another point on the board and we’ve got to keep going. The teams above us aren’t going to win every game so we’ve got to make sure we do better than one or two of them.
“The goal we conceded was very disappointing. For the majority of the game the performance was better than Morecambe’s.
“We’ve just got to be more ruthless and clinical and we need to stay switched on.” The Exiles opened their account when Tozer tapped the ball into the back of the net following a through-ball from Frank Nouble. But the visitors were a threat on the counter-attack, with Scot Bennett given a yellow card for a cynical pull-back on Adam Campbell.
Padraig Amond came close to extending the lead on the stroke of half-time but his close-range header was cleared off the line. But the Shrimpers applied far more pressure in the second half and were awarded a penalty when Mitchell Lang was brought down in the penalty box.
Rose smashed the ball into the back of the net to level the scores and set up a tense finish. Newport pushed for a late winner but could not breach a resolute Morecambe defence.
“It’s a tough place to come and Newport are a good strong side that are good what they do,” said Morecambe manager Jim Bentley.
“I thought they out-battled us in the first half but we were a lot better in the second half. On the whole I thought it was a fair result.
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