The club are seven points outside the top three in the Scottish Premier League as a result of the defeat.
The manager told Sky Sports News: "I think that is it over for Europe. Realistically, it would be very difficult for us.
"I thought it was a game we had to win and I'm very disappointed with the way it panned out, especially with the sending-off.
"The first goal is always crucial when you come here, the way they play and defend. It's difficult."
United were left with just 10 men on the pitch after Barry Douglas was sent off in the second half.