The Tangerines were held to a 1-1 draw by Ross County on Saturday in the Clydesdale Bank Premier League and have not won at Tannadice now since last August.
Mackay-Steven gave Peter Houston's men the lead early in the second half before Richard Brittain levelled late on, but the United winger is sure they are on course to hand an opposition side a thumping.
Mackay-Steven said: "I think it's coming. It's been well-documented about how we've struggled so much at home this season but it's got to end some time.
"I think we could give some team a bit of a hiding if we can just get ourselves in front and hold our lead.
"We played well in spells here but it just wasn't to be in the end, but we're not that despondent.
"We'll get our rewards by sticking at our game plan and hopefully things will pat off for us."
Meanwhile, departing United boss Houston refused to lay into his players after seeing them chalk up yet another draw.
He said: "It's incredibly frustrating, but I'm not going to start blaming the players because they give me absolutely everything.
"They're an honest bunch and want results as much as anyone and I have a lot of faith in them.
"We can't dwell on this. We just have to move on to the next game and look to get the three points."
County scorer Brittain reckons they are on course to stay up in their first season in the top flight, but the midfield playmaker is refusing to say how many more points they will need to secure their safety.
He said: "It's difficult to say. Who knows how many more points we need to do it?
"We're playing really well as a unit and that has been the key for us this season, sticking together as much as possible.
"It's never easy coming to a place like Tannadice but I thought we acquitted ourselves really well.
"We've given ourselves something to build on between now and the end of the season, and I'm sure we can do that."