He criticised Budge for not offering the manager greater public support.
"I've not read them [the comments] but I’ve heard from a few people,” Neilson said.
"I know Steven well and he's a passionate guy. He's very passionate about football management and also passionate about Hearts and Scottish football.
"Everyone's entitled to their opinion and it's part of being a manager. people will talk about what's going on and the ins and outs as soon as you drop a couple of points.
"The board, Ann, Joe and everyone at the club have been really supportive. They understand football, and especially at a big club like Hearts, when you lose a couple of games there's always going to be negativity.
"It's about getting everyone singing from the same hymn sheet. The first objective is to get back in the top flight then build the team again over the summer.
"A lot of the time, people want instant success and it’s got to be done yesterday.
"We're trying to move this club forward so there's going to be a few steps forward and a step back.”
Part and parcel of management
Neilson has come under increasing pressure in recent weeks from fans who are unhappy with the direction they see the club going in.
Hearts, who could secure the Championship title this weekend, have won just two of their last nine games in all competitions, including an embarrassing Scottish Cup exit to the hands of Highland League side Brora Rangers.
"It's part and parcel of the game now," Neilson said.
"Your job is to win and if the team isn't winning then you have to take the negativity that comes. But we know we've got a good group of players here, a great support, owner and sporting director.
"It's a case of just getting back to what we were doing three or four weeks ago."