"Outside the club there might have been a little bit of a panic after those first few matches but there was none inside," Giggs told PA Sport.
"I guess the irony is that up until the Chelsea game, we had not played as well in the matches we have won as we did, certainly against Manchester City, when we created an unbelievable amount of chances but still lost."
Although Sunday's win over Chelsea marked the first time United have scored more than one goal in a game this season. But, the Reds' performances have been built on solid defensive foundations.
"Everyone knows the main reason for our recent results is the way we have defended," he said. "At times, we have not played well but we have been resilient and with more positive results comes confidence and form."