The Three Lions headed into Friday's World Cup qualifying encounter at Wembley knowing that their fate rested in their own hands, but aware that any untimely slip-ups could be costly.
Nerves were obvious during a tense opening 45 minutes, but talisman Wayne Rooney provided the breakthrough shortly after half-time.
A reply from Montenegro which brought them back into the tie at 2-1 threatened to provide an unwelcome twist in the tale, but efforts from debutant Andros Townsend and the in-form Daniel Sturridge saw England secure a comprehensive success.
Victory ensures England remain top of Group H and guarantees a top-two finish, keeping them firmly on course for Brazil 2014, and Hodgson admits he could not have asked for much more from his troops heading into a crucial double-header which also includes a home date with Poland on Tuesday.
He told Sky Sports News: "I think they made the country proud.
"I think the way we worked so hard every time we lost the ball, we worked really hard to chase back and win it back again. And of course, luckily, we had some good attacking moments, even in the first half.
"We were up against a packed defence, but that opening goal was very important because it meant that they had to come out a little bit more and it opened the way for us to score some more."
On Rooney, who has now netted six times in this qualifying campaign, and Townsend, who was making his senior international bow, Hodgson added: "It was a good strike at goal (from Danny Welbeck in the build-up to the opener).
"The goalkeeper couldn't hold it and I was a bit concerned at one moment that the ball had slipped away from Wayne, but he did well to hook his left foot around it. That put us on the path, really.
"At 2-0 we had some fabulous opportunities to score a third goal - there must have been four or five really good opportunities where we were very close to scoring. And then suddenly we have the cold shower of that deflected goal.
"But fortunately for me tonight, fortunately for the nation and fortunately for Andros himself, he stepped up to the plate and scored a fantastic goal which gave us the chance to see the game out quite comfortably."