The Black Cats have taken seven points from their last three games - drawing with Manchester City before beating Chelsea and Cardiff - to boost their survival hopes with three games remaining.
Gus Poyet's men have a game in hand over 18th-placed Norwich, who they sit above on goal difference, as the Wearsiders prepare for a trip to Manchester United before hosting West Brom and then Swansea.
Their 2-2 draw at the Etihad Stadium ended a run of five straight defeats and Giaccherini, who set up both goals that night, thinks the result over Manuel Pellegrini's side was the catalyst for their upturn in fortunes.
"For me, our mentality changed at Man City," he told the Sunderland Echo.
"That draw made us stronger mentally and from there, everything has changed.
"We need to continue like this in the next game at Manchester United. We will go there to win.
"We have good memories of going there from the League Cup, but we can't think about that game. This is a different game. Manchester United have changed managers and they will be very difficult.
"It was very, very important to win against Cardiff because they are directly around us.
"Now we've got seven points from the last three games which is fantastic. We think we can stay up going into these final three games."
Giaccherini came off the bench in the vital 4-0 win against Cardiff to net his fifth goal of the season before assisting Wickham for the fourth, and he says he is glad to be heavily involved again after starting just once in the league since New Year's Day.
"In the last two months, I haven't played much. I don't know why," said Giaccherini.
"But the last three games have been important both for me and the team.
"The team has to come first because we need to survive in the Premier League.
"But it's good for me to do well, for the consequences it could have with me for the national team.
"I'm happy to contribute with a goal and for us to win. The other times I've scored in the Premier League, were one draw and two defeats."