Bowen canceled out Michael Keane's opener for Everton on the night.
The Hammers skipper said at the final whistle: "It's a big point for us, I think we had chances to win the game. I think they had chances as well, so on reflection probably a fair result.
"It speaks to the character of the team, going down 1-0, and we said at half-time it's only one goal, whether it takes us until 90 minutes, 95 minutes, and we knew we'd get our chances. And in the end, we defended well when they were pushing for a winner, and we were as well. Not a bad result."
On his goal, Bowen continued: "Just try and get in the box and when it falls. When I get in the box, I know what I'm going to do before the defenders do. It's just about hitting it towards the goal, and tonight it went in for me, so really happy with that.
"We've got a really good group here that really want to work hard and change our fortunes, and I think you saw that tonight. We've had Nuno for two days and I thought we put in a really good performance, so it's about time, about putting the work in and listening to the new gaffer and we've got a group that wants to work and wants to do well, so we're heading in the right direction and tonight's a good start for that."