Ludogorets claimed their first UEFA Champions League victory thanks to full-back Yordan Minev, who gave the Bulgarians a 1-0 win in the first minute of stoppage time.
Basel were up against it early on at Natsionalen Stadion Vasil Levski in Sofia following Serey Die's red card in the 18th minute for a challenge on Cosmin Moti.
While the result was not ideal - with Basel now level on three points with Ludogorets and Liverpool - Sousa was still proud considering the circumstances.
"In the second half it was much harder for us," said Sousa. "Ludogorets pressed hard and created several chances, but we played very well at the back.
"We controlled the last few minutes, committed men forward, but one counter attack killed us.
"I am very proud with the way we played but obviously disappointed with the result.
"The group is very competitive, anything is possible. We still have two games at home. The fans will vital, like they were against Liverpool."
Basel midfielder Fabian Frei felt the visitors deserved a point.
"Everything went wrong. There are days like these, we have to accept that," he said.
"We fought for 90 minutes to take a point with ten men and I think it would have been a deserved point in the end.
"We went into this game aiming to win, to keep the ball. Then we got this red card and everything changed."
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