The Merseyside club scored twice in the dying minutes to force a 3-3 draw with the Red Devils and Cahill, who scored and set up the final two goals, is of firm belief the result can get things going for the winless club.
"I could see some of our fans leaving at 3-1 and I was thinking that we don’t want to let these people down," Cahill told the Liverpool Daily Post.
"In that situation you try to find anything. We found it against United and we need to push on now.
"The only thing missing in the previous three games was the goals, but our belief has not been effected. It would have been easy to lose belief at 3-1 but we kept going.
"Now we need to eradicate the mistakes, we have been creating our own problems. It’s only the start of the season and we have a lot to do. Hopefully this can be a launchpad for the season."