Adam Armstrong struck on 85 minutes to earn the 1-0 win - a first in the Premier League for Martin.
"It was a big relief, happiness, gratitude and pride in the players and the staff and the supporters and the owners and the board," said Martin.
"We've been in a really tough period so for the guys to stick with... you guys spend a bit of time at the training ground and stuff and it's never felt any different.
"The cloud of not having a win has hung over things but the way they work, the way they train and the way they interact with each other, they're amazing.
"They're an amazing group to work with. I love them and I love being here so I want to drag it out for as long as I can. A win will certainly help that.
"I think some of the football we played today was outstanding. A few sticky moments when they took the ball off us because they were well-drilled.
"We recovered well from them and everyone stuck at it and we scored a goal from brilliant courage and composure in our own box.
"Defending the set play, we head it down rather than clear it and play a one-two together for Matty Fernandes to drive up. I'm really proud of the players."
"The players have been criticised so much sometimes for stuff they're trying that hasn't quite come off so I hope they get some credit when it does go right."