Defender Juwon Oshaniwa insisted at the weekend that he has not come to Scottish football for a picnic and that the Jambos are genuine league contenders.
However, eager to play down his side’s chances of challenging Celtic, Neilson has spoken to Oshaniwa and his other players in a bid to ensure they are not forced to eat their words further down the line.
Five wins from five, with hugely impressive performances, have taken expectations through the roof in Gorgie, but Neilson is trying desperately to calm the excitement that has clearly infiltrated even some members of his high-flying side.
Yet the Tynecastle head coach knows it is a fine balancing act he has to perform with players brought to the club specifically because of their positive outlook and strong mentalities.
He said: “Juwon’s a confident boy and he’s won things before; he’s won the African Cup of Nations, which is a huge tournament and far better than the Scottish Premiership.
“I’ve brought winners here and I want winners, I want guys that want to win things.
“But we still need to be realistic as to where we are. I’ve spoken to Juwon about it and to the rest of the players about just keeping things under control. We need to be realistic about where we are. The media’s all jumping on the bandwagon after five games.
“But is anyone going up to Aberdeen telling them they’re going to win the league? They’re undefeated and have a game in hand, and can go ahead of us if they win their game 3-0.
“From our perspective, we don’t talk about it in the dressing room – we don’t. We just talk about what we’re going to do on the Saturday or the next day or in the next game. That’s it.
“The players understand that. They dealt with it like that last season and they’ll do the same this year.”
While he may be keen to hold back hopes of league success, Neilson has a different approach to this evening’s League Cup encounter away to League 1 Forfar.
He added: “We’re trying to get through because it’s a competition we want to progress in. Every competition we go into trying to win it and the League Cup is exactly the same.
“We want to try and go as far as we can. It’s good for the fans, it’s good for the club, financially, and it’s obviously a chance for the players to win something.”