The Magpies had to wait until the 84th minute for substitute Shola Ameobi to fire them in front against the League Two side, and the second-round tie was only 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."
Progression in the cup was the bare minimum with those fans who travelled to the Globe Arena and many more back at home on Tyneside in open revolt over the club's summer transfer activity, or more accurately, the lack of it.
Pardew was not commenting on reports that they have re-opened talks with Lyon striker Bafetimbi Gomis and made an inquiry about a loan deal for Chelsea's Demba Ba - finance is currently an issue with the latter - while Yohan Cabaye's future is yet to be resolved.
Pardew made wholesale changes as he used the depth of his squad, but his under-studies struggled at times to impose themselves.
Gosling had to make goal-line clearances from Mark Hughes and Padraig Amond, while keeper Rob Elliot twice had to deny Amond, all before the break with the visitors offering little in return.
Pardew introduced Shola Ameobi at half-time and saw him pass up a glorious 49th-minute opportunity, but it was Hatem Ben Arfa's arrival which sparked a concerted assault with the Frenchman setting up both Ameobi brothers to score as time ran down.
Asked about the older Ameobi's contribution, Pardew said: "He's actually looked the best I have seen him in this pre-season. I think the Nigeria selection has actually given him a boost, I can see that in his eyes.
"He is looking forward to the international coming up and I think that's benefited us.
"Sometimes we moan about that; this time it's been a bit of a lift for him and his confidence and everything. He was terrific in the second half."
Newcastle's reward is a home tie against Sky Bet Championship Leeds in the third round, and that will reunite Pardew with Brian McDermott, the man to whom he gave his big chance during his time at Reading.
He said: "My old mate Brian McDermott is there and I will be looking forward to welcoming him, and I'm sure Leeds will be looking forward to coming to us.
"The thing I am most relieved about is the home tie, thank God for that. I think it's the first one I've had since I've been here!"
Morecambe boss Jim Bentley was left to reflect on what might have been, but was delighted with his team's efforts on the night.
He said: "At the end of the day, we have given a great account of ourselves. I think we were the better side in the first half, we just needed to score when we were on top.
"It could have been a whole different ball game. Their crowd might have got on top of them a little bit, it would have given us that little bit more confidence.
"But we gave a good account of ourselves, we had a right good go and I am proud of all the players tonight for their efforts."
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- Shola Ameobi