The Seasiders eased into the next stage as they avoided a cup upset against their League Two opposition thanks to goals from Nathan Delfouneso, Armand Gnanduillet, Matty Virtue and Sullay Kaikai.
Morecambe did briefly threaten an unlikely comeback when Cole Stockton scored in first-half stoppage time to make it 3-1, but Grayson's men did what was required to get the job done.
“I thought it was a decent game and Morecambe played well again today," Grayson said.
“They gave us a good game in the EFL Trophy earlier in the season, so we knew we had to be right with our attitude.
“We knew we’d have to play with a purpose, an intensity and try and replicate a similar type of performance we produced last week against Peterborough.
“For large parts we did okay, but I’m frustrated we conceded a needless goal on half-time which could have given Morecambe a big lift.
“But we were professional in the second half and I felt with our shape we’d get some more opportunities to kill the game off - which we did.
“The scoreline was probably a bit wider than the game suggests, but we still had some good opportunities to score a few more as well.
“We had to be professional and that was the key word at half time.
“That goal for Morecambe just before half time will have given them a lift and from my point of view I had to make sure it didn’t affect us in the second half.
“If Morecambe get the next goal in the game it then becomes a real cup tie.
“We changed it around a little bit midway through by going to a back four and bringing Ollie Turton on.
“We still looked a threat and created some good opportunities, with Sullay having a chance just before he scored.
“But we’re through to the next round and that’s all we wanted before we started the game today.”