Torino's fans made their feelings known at the end of a 0-0 draw between their side and Genoa in midweek with a lack of competition on the field and the general feeling that both sides were happy with a point in view of Palermo's defeat to Udinese at the same time.
A draw would do for Torino in Verona on Sunday too, but Corini insists he will not be settling for such a result.
"It's definitely not going to be just a walk in the park," he said. "We want to get a win to finish this season on a high.
"We want our fans to witness a great performance and we will be looking for a convincing result both tomorrow against Toriono and then next weekend against Atalanta in Bergamo.
"There are still six points to be played for and the aim, in general, has got to be to try to raise the bar.
"Now we are safe, we are aiming to end in the top half of the table."
Victory or not, Corini has already done what he was hired for by saving the Flying Donkeys from relegation.
His temporary contract after replacing Domenico Di Carlo expires in the summer, but he does not want to discuss what will happen after next weekend just yet.
"I agree with the club that we should wait until the season is over," he said at a press conference.
"I have my own project in mind which I will present to my club and if we find that we share the same intentions, then there will also be the foundations for a good adventure together."
The future of Torino coach Ventura is not so solid either following the midweek fiasco against Genoa which turned many of his side's fans against the team.
Abandoning the attacking philosophy he has preached all season and seeming to accept a goalless draw has not gone down well with the Granata fans, who will be expecting a return to the roots in Verona tomorrow.
However, striker and captain Rolando Bianchi may miss out due to injury.