The Millers fought back from 2-0 down and looked to have earned a points, but conceded twice in the final seven minutes to go down 4-2.
Harford gave his players an earbashing in the dressing room after the game, statting that the performance was not up to scratch.
He admitted: "They've had a roasting, they deserve a roasting and Southend deserved to win.
"We've got some difficult games coming up and we're thin on the ground, but I'm not prepared to accept that kind of performance.
"We've got to get better, we've got to improve as a unit and as individuals, we won't be able to forget what happened here, and we've got to learn from this.
"We were simply not good enough. I thought we were fortunate to get back to 2-2 and we could have been 5-2 down after five minutes of the second half.
"I am extremely disappointed. I've asked the players what went wrong. To be honest, we were all over the place."