Saints found themselves 3-0 down before half-time as the hosts proved much the hungrier side in the Tayside derby, and Jackie McNamara's men then cruised to their first win of the new Scottish Premiership campaign.
Pre-match fears were confirmed for Wright as he watched the hosts take command from the first whistle and run out convincing winners with goals from Keith Watson, David Goodwillie, Gary Mackay-Steven and Stuart Armstrong.
Wright said: "To be honest, I did see it coming before the game. We were very flat in the dressing-room.
"I said to them that I didn't want them to come in at half-time and me having to give them a rattle. And those were pretty much true words as that's what happened."
Wright promised to take some responsibility if he feels his own preparation work played some part in the heavy defeat.
He said: "There was a severe lack of energy and zip about us today and that goes for our work off the ball as well. That was very disappointing.
"As the manager, I will look at what we did this week along with the staff to see if maybe we contributed to that a little bit.
"United won a lot of second balls so we'll look at it again and speak to the players on Monday and see how they felt."
Saints had been roundly praised for their 4-0 win over Ross County, and Wright insists his men will respond in the right way to their loss.
He said: "We'll take it on the chin. That's football for you after all the accolades we got last week for beating Ross County.
"It was always going to be important to get the first goal, particularly against a side like Dundee United who have a lot of good players.
"We emphasised the importance of not giving them a lift which they drew confidence from as soon as it went in.
"There was a huge slice of good fortune about the first goal which took a deflection as Steve Banks had it covered easily.
"We made it hard for ourselves but it wasn't a 3-0 game at half-time.
"We'll learn from it though and move on to the next game."
United manager McNamara said: "It was a good win for us. We scored the goals at a good time and we took confidence from that.
"I'm delighted for David Goodwillie to get his first goal. I thought his all-round play was much better. He looked a threat.
"We were up and at them today. We didn't want to get into a fight with them and play for second balls. We wanted to get the ball down and play which is what we did well."