Derby's players all ran to the linesman to protest but referee Darren Deadman allowed the goal to stand.
Manager Nigel Clough said: "We were very aggrieved by the manner of their equaliser.
"We all felt it was handball. Although we didn't have a good view you always know from the reaction of the players on the spot.
"When seven or eight players all immediately show they are convinced it's handball you know that's what's happened.
"In the dressing room they all confirmed it was handball. There are four officials out there and surely one should be in a position to see that.
"Defeat would have been a travesty and we weren't happy about their second goal. We felt DJ Campbell was repeatedly fouled but we made the mistake of having too many people forward with 93 minutes on the clock."
West Brom manager Roberto di Matteo did not have a good view of the incident but said: "From where we were standing it looked a valid goal.
"The linesman gave it straight away, he did not hesitate at all. We couldn't see but I guess it went in off his body or thigh.
"But if I reflect on the whole game I think it was a deserved draw for Derby. We knew we were going to be in for a tough afternoon because they are a good side at home.
"I think that you take a point but we are disappointed because we were so close to getting all three points.
"Looking at the second goal we conceded we are disappointed because lately we have been defending much better than that."
Derby's performance certainly merited a share of the spoils after they had denied West Brom the time and space to construct their impressive passing game.
Although Cox struck the outside of a post early on, Derby were well worth the lead given to them in the 41st minute when Paul Dickov turned on the edge of the box and scored with a shot which deflected off Jonas Olsson and the underside of the bar.
Derby were inches away from a second when Rob Hulse just failed to connect with Robbie Savage's low cross in the 50th minute but West Brom equalised when Brunt delivered from the right and Cox forced the ball home.
The visitors appeared to have stolen the points in the 90th minute when Gonzalo Jara dispossessed Campbell to start a swift counter attack which was finished in style by Graham Dorrans with a rising drive at the near post.
But Derby refused to lie down and in the fourth minute of stoppage time substitute Lee Hendrie crossed from the right and Campbell headed in his first goal since his loan move from Leicester.