The Blues, currently sitting third, host fifth-placed Spurs at Stamford Bridge on Wednesday and Cech is eager for a win which would send the club four points clear of fourth-placed Arsenal and six ahead of Tottenham.
"It was a massive moment," he told Sky Sports after the Old Trafford triumph.
"After the results yesterday (Saturday) we knew we had to win. We have another massive game on Wednesday against Tottenham and we go into it three points ahead of them.
"If we win the game then we will definitely leave them behind, so this was a massive moment and changed the preparation for Wednesday as well.
"During the game you could see how much it meant for us, for them it was a prestigious game but I found the pace a bit slower than usual. But we did really well to come here and win."