Wright also aimed a barb at United's reputation for attacking football by saying he had yet to see them "in full flow" because his team had generally closed them down over the teams' four SPFL Premiership meetings this season.
United will have a 28,000-strong support inside Parkhead today, while St Johnstone will have just more than 15,000. Wright's view was that the underdogs would be favoured by most neutral supporters, especially given that the Perth club was aiming to win the Scottish Cup for the first time in its 130-year history.
"I think most neutrals want us to win the game," he said. "A lot of people have told me. When I was going to games between the semi-final and now a lot of people were saying they like Dundee United but they want to see us win. I think that's maybe natural, because we haven't won it. The chairman and his dad [Steve Brown and Geoff Brown, the previous chairman] have a lot of friends in football and people want to see us win the trophy for them.
"Dundee United are the bigger club and have the bigger fan base. They are taking twice as many to the game, they have won it before, they have been successful and they have had great teams and great trophy winning sides down through the years. From our point of view the pressure is on them. They are expected to win, they are expected to go and win it.
"We are a club that has been run right for many years and are finally getting a chance to get a bit of glory. I think the magic of the Scottish Cup is summed up in the fact that we are in the final. The Scottish Cup has retained that magic, particularly this season. If you look at the FA Cup, I mean last season it was on at 5.30 on a Saturday night and they had league games on. I know times have changed, but I remember growing up as a kid and the build-up on FA Cup final day started at 9am, and they were away at team hotels and stuff.
"It has been overtaken by the importance of the league and Champions League - the game has evolved and changed. But I still think cup competitions should be able to provide that bit of magic and have a fairy tale end. Hopefully, this year that will be the case."
United have reached 88 goals in all competitions this season and scored at least four goals in four consecutive games in November and December. But despite also beating St Johnstone 4-0 in August, Wright claimed those goals were from counter-attacks and he had yet to witness United taking his team apart. St Johnstone won the three subsequent games between the clubs. "I don't know how difficult Dundee United are to play against in full flow, because I haven't seen them in full flow against us. Even in the 4-0 defeat they beat us with counter-attacking [tactics].
"We feel we can set up to stop them being free-flowing. I've watched them in games where they've totally dominated and if you let them do that they'll cause you loads of problems. But I think we've enough about us to stop them being as free-flowing as they have been."