Hamburg's hopes qualifying for Europe next season, therefore, effectively rest on winning the Europa League trophy at their own stadium on 12 May.
"There was no alternative to this," added Hoffmann. "We need to improve the probability of us being successful on Thursday."
Labbadia had admitted that Sunday's performance was "depressing" but angrily dismissed rumours he had lost the dressing room.
"If a team were to play against their coach, then they would also be playing against themselves," he said. "That would make no sense."
The 44-year-old played for Hamburg and Bayern Munich among others during a prolific goalscoring career as a striker in Germany, and won two caps for the national side.
He began his career in management with Darmstadt 98 in 2003, moving on to Greuther Furth before joining Hamburg from Bayer Leverkusen.
Despite their erratic league form, Labbadia had led his troops to the verge of a European final.
They qualified second behind Israeli side Hapoel Tel-Aviv in the Europa League's Group C, beating Celtic 1-0 at Parkhead and drawing with the Glaswegians 0-0 in Germany.
After negotiating PSV Eindhoven, Anderlecht and Standard Liege in the knock-out stages, Hamburg endured a frustrating evening against Roy Hodgson's well-organised west London outfit last week.
Moniz worked as a coach at Spurs for three seasons before leaving in 2008
Labbadia rued his side's profligacy in wide positions after that stalemate but remained ultra-confident they could advance in Thursday's return leg at Craven Cottage.
"Unfortunately, when we did manage to get down the flanks, the delivery was too inaccurate," he said.
"We'll probably have it easier in England, though, because Fulham will be forced to attack. It's going to be very tight, but I believe my team will secure their place in the final."
However, it will now be 45-year-old Dutchman Moniz, a former member of Spurs' backroom staff who followed Jol to Hamburg, who has the task of trying to take the Germans to a decider against either Atletico Madrid or Liverpool.
"He is incredibly enthusiastic, knows the team and English football well and lives for football," said Hoffmann of Labbadia's interim replacement.
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