The Magpies had to wait until the 84th minute for substitute Shola Ameobi to fire them in front at League Two Morecambe, and the second-round tie was only finally settled in injury time when younger brother Sammy claimed a second.
It was a much-changed Newcastle's first win of an already turbulent season, and Pardew is hoping his senior players can repeat the feat in the league when Fulham arrive at St James' Park on Saturday.
The 52-year-old said: "I have just said to the players in there, the club owes a big thank you to Gael Bigirimana and Dan Gosling and Curtis Good for getting us a win because it's going to raise everyone's spirits in the first team.
"It's taken a little bit of pressure off them, the first goals, the first win. Let's hope on Saturday we get a win and then you would have to say that is a start we can accept because four points out of those three games is okay.
"But we have got to win on Saturday and that's what we are going to try to do."