The Gorgie side, sitting third in the Ladbrokes Premiership, allowed a two-goal lead against their Edinburgh rivals to slip in the first meeting at Tynecastle with Paul Hanlon levelling for the Championship side in injury time.
Asked whether the initiative might have moved to the other side of the city - Hibs are favourites with the bookmakers - Neilson told Press Association Sport: “I don’t think so. We are a team sitting third in the Premiership.
“Yes, it’s at Hibs and it’s a derby but we have a strong team, a strong squad.
“I think we showed in the first game, we had a lot of play, a lot of chances and the last 10 minutes changes the game.
“We have to make sure that when we go down there we show that we are a very good team.”
It was an Edinburgh derby baptism of fire for several of the Hearts players including Blazej Augustyn, Juwon Oshaniwa, Gavin Reilly, Abiola Dauda, Arnaud Djoum and Don Cowie and Neilson believes that will make them better prepared for the replay.
However, the Gorgie boss stressed that all his players must keep going for 90 minutes, and perhaps more, if they are to get through to play holders Inverness in the next round.
Neilson said: “We are in a better condition than in the previous derby, players are now used to the game and understand the intensity of what is expected.
“We had a lot of players who hadn’t played in it before, foreign and Scottish guys as well, who haven’t been used to that intensity.
“They know what to do and so we go to Easter Road full of confidence.
“For the first 50 or 60 minutes we played really well, it was after that they felt the game was won and they started to sit deeper and tried to defend the lead.
“But when you play in a derby you have to go at it for the full 90 minutes and not give anyone a sniff of getting back in the game.”
The Jambos’ game against Partick Thistle at Tynecastle on Saturday was postponed due to a waterlogged pitch which Neilson believes could also work in his favour, given Hibs played at Livingston on Saturday.
Several key players rested injuries, leaving Neilson a full squad from which to choose, aside from suspended skipper Alim Ozturk, who picked up the second booking of the competition against Hibs.
Former Hearts defender Neilson said: “We were disappointed not to get the game.
“We were coming off a good result against Ross County and we wanted to continue that in the league against Partick Thistle, a game that we would expect to win, to give us good confidence for Tuesday night.
“The referee decided to cancel it and we have to accept it and it means we can have a freshness for Tuesday.”
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