First-half goals from Enoch Showunmi and Ian Goodison moved Rovers six points clear of the drop zone and left the Daggers languishing just a point above fourth-bottom Bristol Rovers.
Harris said: "The damage was done in the first half.
"We looked a tired side and we did not defend as well as we should have done.
"We had the majority of the play in the second half without causing too many problems. A few of the players have a sickness bug and it left them very weak.
"You need all guns blazing when you come to a place like Tranmere."
Source: PA
Source: PA