The United manager said that despite being behind at half-time to a Laryea Kingston goal, he felt there was no need to panic.
"I tried to alter things to see if we could take advantage of some quality balls into the box, but we didn't do that," said the former Hearts boss.
"We passed the ball well, we defended well. It's maybe a measure of how far the team has come that we expect to win here."
Garry Kenneth and Danny Swanson were sent off late in the game for the visitors.
Levein had no complaint with Kenneth's dismissal but was upset by referee Eddie Smith's decision to red-card Swanson, the 21-year-old signed from Berwick.
"I think Danny Swanson's challenge is exactly the same as the one on Garry Kenneth in the first half," said Levein.
"It disappoints me that there wasn't even a booking in the first half and Danny gets a red card. I think it was very harsh indeed."
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