Liverpool have endured an inconsistent run of form since the appointment of the German but the Reds have managed good results against the so called bigger sides, as evidenced by their victories over Chelsea and Manchester City.
On Wednesday, the Reds claimed another good result against a strong team in Arsenal in the form of a pulsating 3-3 draw and Toure has now admitted that the Anfield outfit have become mentally stronger when the stakes are high.
Toure said: "There has been a big, big improvement recently in our mental strength and that's very important when you're at a big club. You can't ever give up. It will be another massive game against United, and these are the kind of games you can win if you are strong mentally.
"If we can be strong, and the fans push us like they did against Arsenal, that can give us something extra. When you refuse to lose games, you often find yourself winning them."