Victories over Montenegro at Wembley on Friday and Poland four days later would guarantee automatic qualification for Brazil.
Unbeaten England, who top Group H by a point from Ukraine and Montenegro with Poland two points further back, have so far only beaten whipping boys San Marino and Moldova in 2014 qualifying.
A confident Hodgson said he was "convinced", a word he used more than once, that England would get it right when it mattered.
England last missed out on the global showpiece in 1994.
"We've never discussed not qualifying, within the camp we are convinced we are a good team, we are convinced we are good enough to qualify and with two home games to come we are convinced that we will do the job," he said.
"Words like fear, anxiety or concern haven't crossed our minds or lips and I've been very impressed this week by the quality of training.
"I know they will deliver and tomorrow night you will see a very good England team. Hopefully, Montenegro won't be a very good Montenegro team and that will make our task a bit easier."
England have failed to beat Montenegro in their three meetings, including a 0-0 draw at Wembley when the two sides met in European Championship qualifying in October 2010.
Montenegro have been hit by a string of injuries, with captain Mirko Vucinic among those doubtful, but Hodgson said it would be foolish if England went for broke.
"It will a more difficult task for us if we adopt a gung-ho approach and suddenly find ourselves a goal to nil down.
"That will complicate the task enormously. I'm very confident that the team I have will strike the right balance between attacking and defending and that we'll cause Montenegro plenty of problems with our attacking play but at the same time be as difficult to score against as we were in the Ukraine (a 0-0 draw last month).
A second-placed finish in the group would result in a two-legged play-off in November and Hodgson predicted there would be big teams who would miss out on the finals.
"Lots of good teams won't get to Brazil next year but I'm convinced it won't be us," said the manager, pointing out England's good recent record at Wembley, with one defeat in their last 13 in the capital (to the Netherlands in a frienldy last year).
"That's quite a nice statistic. I'm fortunate not to have tasted defeat there yet.
"I trust in the team and I'm excited tomorrow night we can show what we can do and I'm convinced we'll put on a very good performance."