Villa, who begin their Intertoto Cup campaign next week, were made to pay for conceding two penalties in Zurich.
Sidwell made his debut following his move from Chelsea but otherwise it was an unhappy afternoon for the tourists, who fell behind early on when Martin Laursen felled Florian Stahel in the box and Almen Abdi converted the penalty.
Gabriel Agbonlahor looked to have levelled almost instantly but his volleyed effort from Marlon Harewood's right-wing cross was offside.
Agbonlahor got one that counted in the 17th minute, powering his way into the box and slotting a low angled drive beyond Johnny Leoni.
Villa wasted more than one chance to take the lead, partly thanks to some excellent goalkeeping from Leoni.
And they were made to pay when Zat Knight brought down Admir Mehmedi with 11 minutes remaining and Abdi slotted home the winner.