The Norwegian has endured a difficult time of it so far at Celtic Park, with his new side far from convincing early in their UEFA Champions League second qualifying round tie against KR.
While they eventually progressed 5-0 on aggregate against the Icelanders, Deila's men have since lost friendlies to St Pauli and Tottenham while also going down to a 4-1 defeat in the first leg of their third qualifying round tie with Legia.
Celtic took the lead in Warsaw last Wednesday, but then shipped four goals - with Efe Ambrose also getting sent off shortly before the break - with Deila accusing his players of losing their heads.
"Worst of all is the commitment and the energy. That’s what concerns me most," he said afterwards.
Deila will look for a much-improved showing in Glasgow on Wednesday, while Feyenoord - who beat Celtic in the 1970 European Cup final - also have work to do to against Besiktas.
The Dutch giants trail 2-1 to their Turkish opponents but have a fighting chance of progression thanks to Mitchell te Vrede's late penalty in Rotterdam.
Zenit suffered a surprise 1-0 defeat to AEL Limassol last time out but will have home advantage against the Cypriots as they seek to turn the tie on its head, while Red Bull Salzburg also trail by a goal against Qarabag.
The Austrian side are bidding to reach the Champions League group stages for the first time but were beaten 2-1 in Azerbaijan, although French side Lille have no such worries - boasting a 2-0 lead against Grasshopper.
Ludogorets against Partizan, Panathanaikos versus Standard Liege and Copenhagen's tie against Dnipro Dnipropetrovsk all remain goalless and in the balance.
Maribor and Dinamo Zagreb hold 1-0 leads over Maccabi Tel Aviv and Aalborg respectively, and Ibrahima Sidibe's goal separates Debrecen and BATE midway through their tie.
David Lafata will hope to continue his fine goalscoring form in Europe this season and help Sparta Prague progress against Malmo - the Czechs leading 4-2 from the first leg - while HJK and APOEL are tied at 2-2 after the first leg.
Aktobe remain in with a shout against 1986 European champions Steaua Bucharest after a 2-2 draw in Kazakhstan, while Slovan Bratislava renew acquaintances with Sheriff having beaten the Moldovans 2-1 in Slovakia.
