Murillo gave Forest a first-half lead before Newcastle fought back to win via goals from Alexander Isak, Joelinton and Harvey Barnes.
Howe said afterwards, "It was difficult but we knew it would be. They are a difficult team to play against because they don't concede many chances and you're left fearing the worse when you go behind. We had work to do at half-time but credit to the players because the second half was up there with our best performances this season.
"Everything we didn't do in the first half we did at the start of the second half. We were intense and direct with our attacking. We asked more questions and could have scored. I'm really pleased with the second half.
"We need our attacking players to contribute goals and Alex has done that in the past few weeks with massive moments, then Joelinton and Harvey Barnes pop up with moments too. We know we have players who can make that difference and I'm really pleased with that side of our game.
"Harvey Barnes did what he does. He's an outstanding player. Trying to find room for him in the team is something that I am conscious of. I'm really pleased he got that goal - I thought it was a fantastic finish."