Tyrone manager Mickey Harte says that they failed to capitalise on their supremacy.
Armagh surrendered their Ulster title when they went down to All-Ireland champions Tyrone at Clones.
Tyrone had looked to be coasting to a big win as goals from Stephen O'Neill and Conor Gormley had them 2-6 to 0-3 ahead early in the second half.
But Armagh staged a gutsy revival and a Ronan Clarke goal helped them pull back to within two points, but Tyrone then replied with three unanswered scores.
Gormley was sent-off near the end for a second yellow card offence.
Tyrone will face Derry in the Ulster semi-finals on 21 June.
Armagh manager Peter McDonnell expressed satisfaction with his side's performance despite defeat by Tyrone.
Mickey Harte's men had taken a long time to get going and found themselves three points to one down in the early stages.
Brian Mallon pointed for Armagh after just 20 seconds and midfielder James Lavery surged through the middle to kick over another.
O'Neill registered Tyrone's first point from a free but Steven McDonnell, playing his 50th Championship match for Armagh, replied from play.
Tyrone had been guilty of a series of wides, but then the points completely dried up for Ulster title holders Armagh.
Sean Cavanagh scored from play, Tommy McGuigan landed a free and then Joe McMahon converted a 45 to put the All-Ireland champions into the lead for the first time.
O'Neill's goal was the score which put Mickey Harte's men in command, although it did stem from a mistake, when Davy Harte went for a point but pulled his shot well off target.
O'Neill did superbly to gather in the loose ball and then turned to beat defender Andy Mallon before drilling a low shot post Paul Hearty at the near post.
Four-time All Star Sean Cavanagh then powered forward to clip over the points which put Tyrone 1-5 to 0-3 ahead at the interval.
When Owen Mulligan sent over another point, and Gormley struck his 40th-minute goal, the game looked over as a genuine contest.
Gormley kept his cool superbly to round Armagh keeper Paul Hearty to leave the All-Ireland champions with a commanding 2-6 to 0-4 lead.
But to Armagh's credit, they hit back and Clarke's goal, added to by two Aaron Kernan frees, one from Steven McDonnell and Brian Mallon's score from play pegged it back to 2-7 to 1-8.
Just when the momentum seemed to be with Peter McDonnell's underdogs Tyrone showed their experience and quality with points from O'Neill (2) and Brian Dooher who had come on as a substitute.
O'Neill's last point simply oozed class as he cut inside a defender before drilling over a superb left-foot score.
Replacement Stephen Forker and Aaron Kernan got points for Armagh but they could not find the room for the goal which they needed.
Tyrone: J Devine; PJ Quinn, Justin McMahon, R McMenamin; D Harte, C Gormley (1-00), P Jordan; K Hughes, E McGinley; M Penrose, T McGuigan (0-02, 2f), Joe McMahon (0-01, '45'); S O'Neill (1-03, 2f), S Cavanagh (0-02), O Mulligan (0-01). Substitutes: B Dooher (0-01) for McGuigan, C Cavanagh for Penrose, Sean O'Neill for Justin McMahon, N Gormley for Joe McMahon, C Holmes for Hughes
Armagh: P Hearty, A Mallon, B Donaghy, B Shannon, F Moriarity, C McKeever, A Kernan (0-03, 3f), K Toner, J Lavery (0-01), P Duffy, M O'Rourke, B Mallon (0-02), S McDonnell (0-03, 2f), R Clarke (1-00), K O'Rourke. Substitutes: S Kernan for Duffy, T Kernan for K O'Rourke, S Forker (0-01) for M O'Rourke, A O'Rourke for Moriarity
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