Neilson began the mind games in the aftermath of last night’s first leg 0-0 stalemate at Tannadice, where the Championship hosts matched their visitors without having that killer instinct in the final third.
Neilson, whose side won in Paisley in the Scottish Cup earlier in the season, said: “I was really pleased with the performance.
“We wanted to win the game but if you’d offered me a 0-0 beforehand I would have taken that.
“These games are always edgy but we handled the pressure well.
“It’s now up to St Mirren to handle the pressure of a full home crowd. When you have a gate of three or four thousand fans, then it goes up to seven or eight, sometimes those extra ones won’t back you the same.
“So they will have to deal with that.
“We handled that tonight and they will have to do it on Sunday when we have 1,500 of our hardcore support there making noise.
“The next couple of days are about recovery. We will do everything we can to get fit and ready.
“We’re excited about it now and looking forward to Sunday,” added the Tannadice boss. “It would have been great to take a lead down there but it’s all to play for.
“For me, the pressure is all on St Mirren. They are the Premiership team and they have 90 minutes to retain that.
“We need to try to control the game a bit more. There was pressure and no-one wanted to make a mistake.
“Going down to St Mirren, there is less pressure on us.”
Saints boss Oran Kearney, pictured said: “I don’t think it makes us favourites. It’s 0-0 at half-time and that’s how we’re approaching it. Our boys handled this very well which was the key for me. They put in a good performance and kept a clean sheet. Now we’re looking forward to Sunday.”