As a youngster at Old Trafford, he was invariably drafted into the side for the competition, as per Sir Alex Ferguson's policy.
"It was always the young players that played in it at Manchester United and it gave them an opportunity so it was a great experience," says Luke.
"At West Ham we have got a really good squad and when you saw what happened with Millwall last year in the FA Cup there is always the chance of putting a run together - and if you get to Cardiff at the end of it it would be fantastic."
Not that Alan Pardew has the luxury of bringing youngsters in the side just for the sake of experience, but he might give Trent McClenahan, who made his debut on Saturday at Crewe, a run if Hayden Mullins does not recover from injury.
Luke, who played in front of him on the right, reckons he has the potential.
"I thought he did great in the game; they brought a tricky winger on and I thought Trent played him well and had a great debut.
"I had a word with him; he is one of a few fantastic young players that hopefully will break through this season."
Looking at the win over Crewe, he adds:
"It was a great win for us; we had a good first half hour and then they nicked a goal, which was sloppy all over the pitch from us.
"In the second half I thought we played very well until they scored and they put us under a bit of pressure - but at the end of the day we got the three points."
It was Luke's first start, and he says:
"It is great to play the first 90 minutes for the club so I am really happy about that; I have come on in the last couple of games, and now I have had a start I will hope to do so in the next game.
"Hopefully I have done enough, but it is up to the manager - he picks the team."
Luke says it was vital to bounce back after the defeat by Wigan and he explains:
"I think we owed a performance like that after the previous game - we definitely showed a lot more spirit than we did against Wigan."
The match, though nerve-wracking at the end, was quite a spectacle and Luke says:
"I think you always get good football against Crewe, and that is what West Ham are famed for, so it was a great match to play in.
"You get battles in all leagues but Saturday was more of an attractive game."
As for his own situation, he concludes:
"I am really enjoying it at training and everyone has made me feel very welcome."