Ireland's hopes of a Grand Slam, following back-to-back wins over Scotland and Wales, were dashed as Eddie Jones's men ran out 24-12 winners.
The visitor was up against it from the moment George Ford capitalised on Johnny Sexton's error to score the opening try after seven minutes, with the Ireland fly-half enduring a rare off-day.
Sexton's error-strewn display, which included two woefully miscued penalty attempts, summed up Ireland's afternoon as Farrell's charges came up well short.
"Disappointing. I think the scoreline flattered us a little bit," Farrell told BBC Sport after seeing Andrew Porter's last-gasp converted score narrow the gap.
"We started firing a few shots when the game was over and that's not what we want to do.
"I think it was a knock-on effect of cumulative errors. The opposition had something to do with it obviously, they played really well.
"They played like a side that was desperate to stay in the competition, so fair play to England for that. But we'll look at ourselves for the reasons we allowed them to play the game they wanted to play.
"First and foremost, I look at myself. Why were England up for it, winning the physical edge? That's down to myself.
"The reality is the last try at the end allows the points difference not to be too bad and we're in the competition.
"We go into the Italy game knowing what we've got to do. If we perform like we want to in that game we'll take it to the last weekend."
A strangely out of sorts Sexton admitted Ireland had nowhere to hide after a lacklustre showing.
"We gave a very good team two tries from our mistakes, not covering the chip kick, and then we didn't take our chances," he said.
"We were getting the ball on the back foot, trying to get to the edges and we couldn't, looked a bit silly at times.
"We still have a big home game against Italy and if we can do that we still have a championship to play for.
"We need to be a bit better, not play in certain areas of the field when we are going backwards."