Second-half goals from Jordi Gomez and Victor Moses added to an early own goal by Sam Collins to give the final scoreline a slightly flattering look.
Martinez said: "I am very pleased with many aspects. We showed energy and performance and we are starting to do things we were working on in the summer.
"In the Premier League we've been doing good things but at the wrong time. Today we did it at the right time and we are slowly gelling together."
One bleak spot for Martinez was a last-minute ankle injury suffered by substitute Moses which is likely to rule him out of next weekend's trip to Tottenham.
"It's unfortunate that we picked up a silly injury at the end and that is a big negative point. It was a really nasty tackle from behind but it's too early to tell the extent."
Hartlepool caretaker-boss Mick Wadsworth described the final scoreline as harsh. Wadsworth added: "If you'd have dropped down from Mars you'd struggle to know who the Premier League team was."
Meanwhile, Wadsworth appeared to distance himself from the possibility of taking on the manager's job full-time despite his side's unbeaten start to their league season.
Wadsworth said: "The chairman has got to decide if he wants someone from outside and I'll just carry on until then. I've heard nothing to the contrary.
"I've really enjoyed working here and what I enjoy more than anything is the training ground. I've never worn a tracksuit in my whole life in the dugout. I feel pushing 60 I'm a tracksuit coach."