Sir Alex Ferguson's men had been firmly in control at the top of the table before the weekend, but surrendered some of their advantage after drawing 4-4 with Everton in a thrilling Old Trafford encounter.
Manchester City capitalised by beating Wolves 2-0 to leave them within striking distance of United ahead of next Monday's pivotal derby at the Etihad Stadium.
If City win they will go above their rivals on goal difference and there will only be two games left for each side, but Mancini remains adamant that United are in pole position.
"Only one team can win this title," he said.
"I've never bet in my life but if you were to ask I would say put your money on United, 100 per cent.
"I don't have a message for Sir Alex. If I did it would only be 'Congratulations for your season and for this title'!"
It remains to be seen whether the apparent mind games being played by Mancini pay off but he is clearly striving to keep the focus away from his players.
In terms of whether City or United are under more pressure, Mancini said: "I don't think they have pressure because they are used to it every year.
"For us, it's different because it's the first time. At the moment, we don't have any pressure because we are not expected to win.
"But we want to finish well. It's important for our season."
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