Roy Hodgson's side got off to an ideal start and Wayne Rooney put them ahead early on, but they failed to capitalise further on their dominance.
The hosts were a different side after the break and Dejan Damjanovic earned them a point.
Gerrard told ITV1: "We stopped playing after the break for 20 or 30 minutes and away from home you can't afford to do that.
"We stopped passing the ball and that's when we lost control and I think they deserved the equaliser."
England featured a relatively inexperienced central defensive pairing of Joleon Lescott and Chris Smalling, but Gerrard did not feel experience had any bearing on England losing their grip on the match.
Gerrard added on ITV1: "I think there was a lot of experience out there and I think the first half we showed that. We controlled game.
"The problem is at 1-0 you're always vulnerable. You've got to go on and get the second goal to get complete control and we never did that.
"They took control of the second half up until the last 10 minutes so they deserved the draw."
It was a draw which meant England remained two points behind Montenegro in the group and have still only won against San Marino and Moldova in the pool.
Gerrard added: "We're still confident we can finish top of the group. We need to win all our games, we certainly need to improve on that second half performance and play like we did (in the) first half.
"We need to put that (not having beaten Montenegro, Ukraine or Poland) right. We certainly need to get three points when go to Ukraine and we need perfect results at home."
England boss Roy Hodgson tried to focus on the positives.
He said on ITV: "I thought our first half was very good, but we obviously did not start the second half as we would have liked to and that gave Montenegro some encouragement.
"But I thought we hung on well and even finished the game quite strongly. Unfortunately in that good spell they got the equaliser and robbed us of the chance of victory here, but all things considered we mustn't be too disappointed.
"It's a long way to go yet and a draw here is something which gives us a chance to build for the future."
England have now draw 1-1 at home to Ukraine and away to Poland and Montenegro.
Asked about his side's failure to win any of those matches, Hodgson said: "Two of them were away from home, that's the way it is.
"We've got three of our last four games at home and the other contenders have got to come to us."