Mowbray and assistant Peter Grant (l) are staring at Europa League exit
Tony Mowbray and his Celtic players were left with a sense of frustration after their goalless draw in Hamburg made Europa League progress unlikely.
Scott McDonald was twice thwarted by keeper Frank Rost and Barry Robson and Georgios Samaras wasted decent chances.
"It's a frustrated dressing room once again. We had clear-cut chances that didn't go in," said Mowbray.
"We could easily be sitting here saying we won this game 1-0. We have two games left and we must take maximum points."
Celtic prop up Group C with two points after four games, with Hapoel Tel-Aviv already through on nine points after their 3-0 defeat of Rapid Vienna.
Media conference - Celtic manager Tony Mowbray
The Austrians, in third place, are now only two points clear of Celtic but, ominously for the Glasgow side, Hamburg on seven points just need a draw from their two remaining matches to move into the knock-out stages.
The tie in the Nordbank Arena in many ways typified Celtic's European campaign this season, with possession too often surrendered cheaply and scoring opportunities wasted.
"Sometimes you're in the dressing room at half-time thinking you needed one of those chances to go in," Mowbray told reporters after the match.
"I feel every game we have played in has been very close, but every other game in the group is 5-1 or 3-0.
"All our games tend to be tight and for whatever reason they haven't fallen our way.
"But you put it into context - they're a very powerful Bundesliga side - and you try to take the positives from it, which are that we are frustrated but we know that we can compete."
Lukasz Zaluska shows in training what a good keeper he is. He's got a fantastic mentality as well
The Celtic manager made tactical changes in the second half in an attempt to break the deadlock, first removing Aiden McGeady and Scott McDonald for Lee Naylor and Marc-Antoine Fortune, then throwing on Niall McGinn for Robson.
Naylor slotted in at left-back, allowing Danny Fox to advance.
"We did go chasing the victory a bit," said Mowbray.
"We put two strikers on for their stature and we kept Fox on to try to deliver into the box, and put McGinn on to use the space in front of us to run the team up the pitch.
"Pat McCourt was the other option but the way the game was flowing I felt McGinn's ability to move at speed away from the defensive areas would help the team more. But good teams force you back."
There was no disguising Mowbray's disappointment that a win had not been achieved but he was boosted by the performance of Artur Boruc's stand-in, Lukasz Zaluska.
Indeed, the Pole may earn first-choice status if he continues the form that saw him make two great saves from a Marcus Berg shot and a David Rozehnal header.
Mowbray added: "Artur is two or three weeks away yet. We'll see how Lukasz performs in that period but he has obviously done himself no harm.
"He shows in training what a good keeper he is. He's got a fantastic mentality as well; he has a lot of respect for Artur."
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