It was a similar scenario to the draw in Poland in October when last night's scorer, Wayne Rooney, also put England ahead before they were pegged back.
But Hart believes such challenges away from home are not easy to overcome and that England have to try and capitalise on a promising position in their remaining games at Wembley.
The Manchester City goalkeeper said: "People ask about not holding on against Poland and Montenegro but they are tough places to come. Hopefully we will look back at last night as a good point earned.
"You've got to give respect to the opposition. I thought Montenegro were great in the second half and they made it hard for us.
"How I do assess the group? It is going to be tough. It is a really tough thing to qualify for a World Cup and you kind of take it a bit for granted.
"That's what we expect as a nation. We are England, we should be qualifying for things but it is easier said than done.
"But that's our plan (to qualify) and it is going to be difficult, but we aim to really capitalise on the home games."
Hart added: "We are not contemplating failing to qualify. That's not even crossing our minds at the moment.
"We've got ourselves in a strong position and we've got Montenegro to come at home and, if we win all the games now, we finish top of the group.
"That's the way we are going to have to view things. We are in this position now so we've got to move on from it."
Hart praised the performance of defender Chris Smalling against Montenegro striker Mirko Vucinic.
He said: "Chris did well, Vucinic is a well respected player, but our boys are not young in terms of experience.
"It's not like we are chucking them out to the lions, they are at good clubs, and have played in massive games before.
"It is another game but at the same time it's nothing new to them."
Hart tried to play down having various objects thrown in his direction during the game.
He said: "You get all sorts of things thrown at you in these games, lighters, marker pens, all sorts.
"Something pinged off my head (a toilet roll) and then wrapped around my shoulders.
"It is not going to kill you is it? It's not ideal but that's the beauty of football.
"The atmosphere was good fun. I thought first and foremost our fans were awesome throughout the game.
"It was a hostile atmosphere and our fans brought colour and good quality support.
"I enjoy playing in those atmospheres."