That point earned England a place at the European Championship in Poland and Ukraine, but their chances of qualifying for the 2014 World Cup in Brazil remain in the balance.
They have now only beaten San Marino (twice) and Moldova, while drawing with Ukraine, Poland and Montenegro.
Hodgson added: "In the second half we lost our control and Montenegro had a good spell, took the game to us, forced a lot of corners and one resulted in their equaliser.
"My overall feeling is one of disappointment because things looked good for us at half-time.
"But it is not a bad result because Montenegro are a difficult team to beat."
Hodgson, meanwhile, defended his decision to make only one change as England deteriorated desperately in the second half, sending on Ashley Young for Tom Cleverley after Montenegro had equalised.
Danny MillsFootball Analyst
Given the pressure England were under, I am surprised Roy Hodgson did not make a tactical change or even a substitution earlier in the second half. He only made one change, bringing Ashley Young on for Tom Cleverley, with 12 minutes to go. He needed to bring someone on to tighten things up.
He said: "The change we thought we would make, and we tried to hold on to make it slightly later, was the one we eventually did make. We had it planned but they scored from a corner kick.
"We thought we would move Steven Gerrard a little bit deeper and get Ashley Young on. I actually thought in the last 10 minutes we did quite well and came in with a few more chances."
Montenegro coach Branko Brnovic conceded that England could have been awarded a penalty in the first half when Danny Welbeck went down in the box, but also argued that Rooney fouled his marker before heading his 35th international goal.
"It is possible that there was a penalty but did you see Rooney before he scored the goal?" said Brnovic.
"I like an attacking strategy, but against England it was not totally the way to go and they showed in the first half how strong they are.
"If we had been complete in our line-up we would have been even more successful."
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