And why should they have. At that point, the home side trailed by 1-18 to 0-14 and many in the near-capacity 29,224 attendance were slipping away, convinced that the affair was over.
They had every right to feel that way. In the second minute of the second half Galway led by two points, 0-13 to 0-11, and were hurling with flair and style. Then they slumbered.
For the next twenty-five minutes it was all one-way traffic with Tipp nabbing 1-6 without reply, and taking a seven point lead.
Galway tagged on a few scores but Tipp matched their efforts, score for score.
Then, suddenly and unexpectedly on 70 minutes, the west awoke.
A long Tony Óg Regan free was greeted with an innocuous little flick on by corner-forward Damien Hayes.
The ball spun in the big hands of the safest keeper in the business, Brendan Cummins, and then hopped out of those same hands and into the net.
Galway were rampant. Hayes and Alan Kerins narrowed the gap to one. Galway hearts were a-soaring. Tipperary hearts were a-racing.
Only the final whistle of Dickie Murphy intercepted what would have truly been a miraculous comeback by Galway, and it was a very relieved Tipp manager Michael Doyle facing the media afterwards.
"I know now me heart is okay! That goal brought them back into it, there was a bit of an onslaught then. After the goal, they got the run on us, and we were delighted to hear the final whistle. Over the whole game however, I think we were the better team, we deserved the win".
They did, just. The irony however was that in their slumber period, and especially after Tipp found the net, the Galway forwards were going for goals when points were there for the taking.
Yet another in a long line of examples then of Galway playing a major role in their own downfall.
The game began at a hectic pace. Galway were on fire in the first quarter and led 0-8 to 0-4 after 18 minutes with the Tipp defence in all sorts of trouble.
Wing-forward Rory Gantley was doing much of the scoring, but corner-forward Kevin Broderick had Thomas Costello in serious difficulty, while Ollie Fahy and David Tierney were also on the board.
For Tipperary flying wing-forward Mark O'Leary was offering the biggest threat but it was significant that dual All-Star Eoin Kelly, Tipp's top scorer for the last three years, was being out-played by the outstanding Ollie Canning.
The Premier are much more than a one-man attack however, and Lar Corbett, after moving to full-forward in the first of several shrewd switches by the Tipperary sideline team, came powering into the game with a hat-trick of points, O'Leary continued to shine, and Tipp brought it back to the minimum at the break as they trailed 0-11 to 0-10.
Galway had the perfect start to the second half also and out-shot Tipperary two points to one (the second of those from the brilliant Canning).
Then, inexplicably, came that valley period. Mind you, if Tipp keeper Brendan Cummins played a significant role in the Galway comeback with that most uncharacteristic error for the goal, his puck-outs were a major factor in this win.
Three points came directly from his deadly-accurate line-drives, while the Tipperary goal, superbly finished by Benny Dunne, also came off a long clearance to the left wing where the game-changing half-time substitute John Carroll was the willing target. He made the catch to set Dunne free on goal.
A good win then for Tipperary in a decent game. Scorers Tipperary: L. Corbett 0-4; B. Dunne 1-1; M. O'Leary 0-3; B. O'Meara 0-2; J. Carroll 0-2; E. Kelly 0-2 (frees); P. Kelly, G. O'Grady, C. Gleeson, E. Enright, 0-1 each.
Galway: R. Gantley 0-7 (0-5 frees); D. Hayes 1-1; K. Broderick 0-2; D. Tierney 0-2; A. Kerins 0-2; O. Canning, R. Murray, O. Fahy, 0-1 each.
TIPPERARY: B. Cummins; T. Costello, P. Curran, M. Maher; E. Corcoran, T. Dunne, P. Kelly; B. Dunne, E. Enright; M. O'Leary, C. Gleeson, B. O'Meara; E. Kelly, D. Byrne, L. Corbett. Subs: J. Carroll (Byrne 35); D. Kennedy (Costello 35); G. O'Grady (E. Kelly 63).
GALWAY: L. Donoghue; D. Joyce, L. Hodgins, O. Canning; F. Healy, T. Og Regan, D. O'Brien; J. Conroy, R. Murray; R. Gantley, M. Kerins, D. Tierney; D. Hayes, O. Fahy, K. Broderick. Subs: A. Kerins (Conroy 47); D. Cloonan (O'Brien 48); D. Forde (M. Kerins 52); E. Cloonan (Murray inj. 64).
Referee: D. Murphy (Wexford). Good job.