Neither Tranmere or Colchester were able to break the deadlock at Prenton Park in a game of few chances.
Rovers dominated the first half, Ash Taylor missing an open goal when his downward header from three yards out hit the ground and went over the bar.
Colchester rarely threatened in the first half, but saw Andy Bond's 25-yard effort comfortably saved by Owain Fon Williams.
With neither side dominating the second half, the game remained goalless.
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Tranmere manager Les Parry told BBC Radio Merseyside:
"I thought Colchester played well. They were well organised and they made it difficult for us.
"We created a lot of chances, and, although we didn't take them, on another day we'll take two or three of those.
"Lucas Akins ran himself into the ground. He's had a really good game. On another day, he'll score a couple of goals too."
Colchester United manager John Ward told BBC Essex:
"We managed to score four goals last week, but I'm probably happier with this result, performance and effort than I was last week.
"Les has got Tranmere working exceptionally hard and, if you don't match that, you'll get beat here.
"We've stood toe to toe with a very good team and come out level, so I'm really pleased with that."