Pope top-scored with 121, his sixth Test hundred, as England were dismissed for 416 on an eventful first day in Nottingham.
But he was dropped on 46 and 54, by Alick Athanaze and Jason Holder.
"I'm happy with the way I went about my stuff and obviously there was a nice couple of drops, which always helps," said Pope, who plays his domestic cricket for English county champions Surrey.
"No one means to drop them but cricket goes in swings and roundabouts. The luck wasn't with me in my county stint.
"I wouldn't say I had doubts but sometimes you think, 'Why's everyone else in the country scoring runs in county cricket but England's number three isn't going out and averaging 50 this summer?'
"That's just cricket for you, you want to go and score a hundred every day but sometimes it doesn't work that way."
Pope, though, was glad to have a "lucky charm' in Arsenal goalkeeper Aaron Ramsdale among the crowd at Trent Bridge on Thursday.
Gunners fan Pope is friends with Ramsdale, a member of the England squad that recently finished runners-up at Euro 2024.
Ramsdale was also in the stands when Pope hit a double century against Ireland at Lord's last year, with the England cricket vice-captain adding: "I'm obviously a big Arsenal fan so I go and support him a fair bit. He seems to be my lucky charm on the cricket pitch as well!.
"He's come to two other games and in one of them I scored 200. It always happens to be the day he's there that I get the runs, so I think he can come more often."
A rare highlight on a tough day for the West Indies, battling to avoid going 2-0 down in a three-Test series, came when Kevin Sinclair marked his dismissal of Harry Brook with a spectacular somersault.
"That's my trademark celebration, from where I come from," said the Guyanese off-spinner, only called into the team on Thursday morning after Gudakesh Motie withdrew because of illness.
"Whenever I get a wicket, I just do it for everyone from there. It all started at the tender age of eight, practising it over and over in the back garden. I know what I'm doing, I've perfected it over the years."
