Celtic have lost their last three matches at Hampden, including their last-four clash against Hearts in the 2012 competition but Mjallby believes his players can shut out talk of their difficulties in Mount Florida.
The Swede told CelticTV: "Hopefully this Hampden hoodoo that we have got right now is forgotten about. We just need to put in a good performance and why not?"
He added: "The confidence should be there because against Hibernian we played quite well and if we put that into the game on Sunday it's going to be hard for Dundee United to live with us."
Mjallby, whose team have also lost to St Mirren and Kilmarnock at Hampden in the last 13 months, added: "It's probably only us in management that thinks about it, not the players.
"You're scratching your head and wondering why because there's no reason why we haven't really performed there.
"It's important for us to make sure the players don't really think about it and just go out and play their normal game.
"If we make sure we defend the way we should defend, we know we have so many good players going forward that we know we will create chances."
Celtic will have Victor Wanyama available for the Hampden tie after the Kenyan midfielder's red card in the 1-1 draw at St Mirren Park last month was downgraded to a yellow by a Scottish Football Association disciplinary panel.