The Turkish Super Lig champions won their first match in eight on Saturday, with Wesley Sneijder's double giving them a badly needed 2-1 home win over a 10-man Karabukspor.
The result lifted them to 10th in the table, and new manager Roberto Mancini is sure to demand more from his squad as the season goes on, starting with their Group B UEFA Champions League encounter against the Danes.
"Sneijder produced the type of performance (against Karabukspor) that we expected from him for the first time," Aysal said.
"Naturally, we have high expectations of him. We have waited for this for months."
The match - which will be Galatasaray's 250th in UEFA competition - will give them a chance to respond to a dreadful performance against Real Madrid in their last home outing in the Champions League.
Galatasaray were embarrassed as Cristiano Ronaldo scored a hat-trick in Real Madrid's 6-1 victory in Istanbul.
They improved in their second fixture, with Umut Bulut's 88th-minute equaliser giving them a point in a 2-2 draw at Juventus.
Copenhagen only qualified the group stages of the Champions League after Galatasaray's rivals, Besiktas, were kicked out for their involvement in a match-fixing scandal.
Stale Solbakken's side lost their play-off to Lille - 2-1 on aggregate - but were placed in Group B after Besiktas were punished.
