The tourists seemed to have a tight grip on proceedings when West Indies, batting first, lurched to 45 for four in the 16th over on Friday.
The home side then slowly worked their way back into the match before Dwayne Bravo (87 not out), Lendl Simmons (65) and Darren Sammy (61) turned on the style in the latter stages to give them a total of 269 for six in 50 overs.
"I wouldn't look too much at our batting - it was the last 10 overs with the ball that hurt us," Broad told Sky Sports television after England finished on 254 for six in reply.
"If we'd given the batsmen 230 to chase we'd have won.
"Up to 40 overs we were fantastic. We put ourselves in a fantastic position but we conceded 100 off the last seven overs and we need to look at ourselves and know how we can get better."
One positive for England was the century scored by left-handed opener Michael Lumb, 34, on his ODI debut.
"It's not all doom and gloom. We lost but we did a lot of good things especially Lumby's hundred," said Broad.
Bravo was named man of the match for his batting exploits alongside Simmons and Sammy.
"It was a great team effort. We didn't start well but then Simmons and myself laid the platform," Bravo said.
"Over 250 runs and we back our bowlers. In the last 15 overs I told the guys we would win the game."
The second match is at the same venue on Sunday.
- Sports & Recreation
- Lendl Simmons
- Dwayne Bravo
- Darren Sammy