The Hammers ended a six-match winless streak with a 1-0 victory at home over Swansea City on Saturday and Cole hopes that can be repeated at Villa Park this Sunday.
"I think Saturday has given us a lift," he told the club's official website.
"Thirty points is a big barrier to get to and now we're all looking up. The next game is Aston Villa - we want to improve our away form and it's important that we get a result there.
"In every game there's pressure and it's so difficult to win in this league as every team gives you different kinds of problems. It really is competitive at the moment and we'll just be taking every game as it comes.
"Aston Villa are a young team and you don't know what you're going to get from them really. They have a lot of talent and (Christian) Benteke is a handful up front. It's going to be a tough game I imagine.
"We need to get some momentum going on the road by getting points on the board."
West Ham currently sits 11th on the table with 30 points whilst Villa are in second-bottom on 21 and have not saluted in their past eight league outings.