Frank de Boer won his first game in charge of Inter Milan 2-0 over Celtic in the International Champions Cup finale at Thomond Park in Limerick on Saturday.
The Dutch coach replaced Roberto Mancini, who lost to Paris Saint-Germain and Bayern earlier in the competition last month, then fell 6-1 to Tottenham in a friendly.
Goals from Eder and Antonio Candreva gave Inter the win over Celtic, who made nine changes from the team who beat Motherwell this week and have a Champions League qualifying clash looming on Wednesday.
The Scottish champions would have been behind early on had Leonardo Fasan not showed good agility to help Benaga's 20-yard effort over the crossbar before parrying away a fiercely-struck Ivan Perisic shot.
In between, the fit-again Dedryck Boyata clipped a shot against the Inter crossbar.
It was end-to-end action and Stefan Johansen cleared off his own line from Andrea Ranocchia's glancing header before Samir Handanovic saved with his legs when one-on-one with Stuart Armstrong.
Fasan then denied Geoffrey Kondogbia just after the half hour but the Italian was eventually beaten as half-time approached when Perisic flicked a lovely header back across goal from a corner and Eder simply turned the ball in from close range.
Celtic responded well to the setback and began the second half brightly. Efe Ambrose looped a header just over and on the hour mark Nadir Ciftci thumped a volley against the crossbar.
It was to no avail, though, and in the 71st minute Inter hit Rodgers' side on the counter attack to extend their lead. Candreva latched on to a lovely through ball from Mauro Icardi before beating Fasan with a perfectly weighted chip.
It was the cue for Inter to sit deep and defend what they had and they restricted Celtic to a couple of long-range efforts from Ryan Christie and another from Stuart Armstrong.