Roy Hodgson's men could fall five points behind Montenegro or one point clear at the top depending on whether they win or lose in Podgorica.
Hart said: "Tuesday is big, an exciting game for us. We are getting closer to the World Cup finals.
"We've got to perform. Maybe we could be accused of taking our foot off the pedal as we let a 2-0 advantage slip away last time against them when we needed just a point.
"That is not going to be the case this time. We've got a job on our hands in an intimidating arena, but we've definitely got the capabilities.
"We go there with the intention of doing well against a good nation. Brazil is a long way off, and I'm not going to get carried away thinking about that, but hopefully with a few wins we can start doing that.
"I treat all games the same. Just because I might have had little to do on Friday, I'm not going to be asleep on Tuesday.
"It's the same build-up, same hype, same adrenalin, whoever you play against."