Celtic crashed out of the Europa League tonight despite seciring their first victory of the campaign.
Hamburg's 2-0 win over Rapid Vienna in the other Group C fixture took them top with 10 points, one more than Hapoel, and made Celtic's trip to Vienna on December 17 a redundant final fixture.
Greece striker Georgios Samaras gave Celtic the lead midway through the first half, as he had when the two sides met in the first section game in Israel in September which Hapoel Tel Aviv ended up winning 2-1.
This time though, the home side added to their lead through a Barry Robson free-kick after the break to run out deserved winners.
However, after taking care of the Israeli side, and on the evidence of the first meeting between the two sides, boss Mowbray and the Celtic fans might wonder why they allowed tonight's opponents to go to through to the knockout stages along with Hamburg.
It was always going to be an uphill battle for Mowbray's side regardless of the boost they received by going back top of the Clydesdale Bank Premier League at the weekend with a win over St Mirren.
The Parkhead men, with only two points from their first four games, had to win their last two matches while hoping that Hamburg lost their remaining two fixtures.
Hapoel, on the other hand, needed one point to all but secure their qualification.
In a peculiar backdrop to the game, the Scottish Trades Union Congress had urged Celtic fans to wave Palestinian flags in a show of solidarity, as a form of protest against last year's invasion of Gaza. That failed to materialise.
A protest, though, came from those disgruntled Celtic fans who stayed away, the stadium being only half-full at kick-off.
The visitors, cheered on by a couple of hundred supporters, had every reason to feel confident, having scored in all their away ties in Europe, including the two qualifying rounds.
And with 12 goals in four group games, they arrived in Glasgow second top scorers in the competition behind Shakhtar Donetsk.
In a subdued start to the match, Scott McDonald had the ball in the net in the fourth minute after Aiden McGeady had split open the Hapoel defence but the striker was denied by the offside flag.
Moments later, only a timely intervention by midfielder Landry N'Guemo at the edge of his own box prevented Etey Schechter breaking through the Celtic defence.
In the 20th minute, McGeady, the most lively of the Celtic players, reached the byline before cutting the ball back to McDonald, whose close-range shot drew a decent save from Vincent Enyeama.
The opening goal almost arrived moments later as the home side slept through a short free-kick, allowing Gil Vermouth to set up Schechter whose volley from 14 yards just cleared the bar.
However, it was McGeady who made the difference in the 22nd minute when he took a quick free-kick from McDonald and raced into the box and past Dani Bondarv.
When his inviting cross came over, the on-rushing Samaras rose high to head in.
The home side were in control and in the 35th minute Enyeama raced out of his goal to intercept McDonald, but the Australia international evaded the challenge, turned and crossed for Samaras whose flick from 12 yards came back off the post.
Robson, who had moments earlier fired a 25-yard free-kick inches over the bar, drove the rebound goalward but the Hapoel goalkeeper got back to block.
Hapoel kept Samuel Yeboah and Zurab Menteshashvili inside at the interval, bringing on Maaran Lala and Nemanja Vucicevic, the two scorers from the first game in Israel.
The changes, if anything, disrupted Celtic and they coughed and spluttered in their attempts to get going again.
News of Hamburg beating Rapid Vienna in Germany had permeated the stadium, leading to some disappointment and frustration in the stands but they soon had something to cheer.
Marc-Antoine Fortune replaced Samaras just after the hour mark and the former Nancy striker was involved in Celtic's second goal in the 68th minute when he was fouled 25 yards from goal by Bebars Natcho.
Robson stepped up and curled a left-footed drive past the helpless Enyeama to secure the points.
Fortune, without a goal since a double against St Johnstone in August, had a close-range shot blocked by Enyeama and McDonald missed a sitter moments later but it was all rather irrelevant.
The campaign had been lost in the previous four games and Mowbray can turn his attentions to regaining the SPL title from Old Firm rivals Rangers.