The visitors failed to get a single shot on target in the first half and Ireland Keeper Keiren Westwood easily saved two chances for Wayne Rooney in the second.
"It's way below what we were hoping to achieve," England manager Roy Hodgson told reporters, pointing to Raheem Sterling in particular as failing to "hit the heights" he was capable of.
"We didn't make nearly enough use of moments when we got into the final third... we have to do better than that," said Hodgson, whose team is leading Group E by six points and plays Slovenia in Ljubljana on June 14.
A subdued Rooney remained on 47 goals for England, two behind Bobby Charlton's record mark.
Both managers praised the behaviour of fans, two decades ago the sides were led off the pitch in the old Lansdowne Road in 1995 after England supporters began throwing missiles, including seating ripped from the stands after their team fell behind.
Relations between England and Ireland have improved drastically since a 1998 peace deal in Northern Ireland, but organisers took no chances, playing the game at 1 p.m. local time on a Sunday with most pubs in the area not open before kickoff.
The tone was set by a standing ovation from both sets of fans for Jack Charlton, an English World Cup winner in 1966 and Ireland's most successful manager. Some England fans applauded the Irish national anthem.
Ireland manager Martin O'Neill, whose side are fourth in European Championship qualifying Group D, said despite the lack of goals, the game was "exactly what we needed" to prepare for a game against third-place Scotland next Saturday.
Strikers Daryl Murphy failed to convert Ireland's best first-half opportunities, striking the ball narrowly past Joe Hart's goal early in the game and heading wide.
Hart was also forced to save a strike from substitute Jon Walters in the second half and Aiden McGeady failed control the rebound.
(Editing by Ed Osmond)
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