The keeper was disappointed that his error cost the Three Lions a vital away win, while Steven Gerrard suggested that a point is a good result with the team not performing well
Wayne Rooney had put his side ahead in Wednesday's game, postponed from the previous evening due to a waterlogged pitch, but the Manchester City goalkeeper failed to claim a second-half corner and was punished when Kamil Glik nodded in the equaliser.
The 25-year-old accepted the blame for the goal, adding that his side having limited the hosts' other chances only added to his disappointment.
"I came, I didn't get there, and the lad's done a good header," the England keeper told ITV. "My fault - I probably should have punched it or stayed in my goal, didn't do either and they scored.
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"I think they played well today but at the same time they were knocking on the door and it weren't going to open, and unfortunately, that was the case."
Gerrard, wearing the captain's armband once again, indicated that a draw was an acceptable result despite a below-part performance.
"I think time will tell, we'll have to see what happens at the end of the group, but it's a decent point but the lads are slightly disappointed," the midfielder observed.
"We know we can play better than that. Especially after taking the lead; we should have seen the game out but it wasn't to be. I believe this point will be a good point at the end of the day but we'll have to wait and see.
"We're disappointed not to take three points today, so our points tally could have been a lot better," he continued, despite the result putting England clear of Montenegro at the top of Group H.
"But this is a tough place to come. Before the game, the conditions, the pitch; I thought they handled the pitch just slightly better than us today.
"That's the disappointing thing, but we're not going to grumble, [we'll] take the point away from here because I don't think anyone in the group will come here and take maximum points.
"It's a tough place to come and they're a fantastic team on the counterattack, as you've seen tonight."