Dean was confronted by an angry Mauricio Pochettino after Ashley Barnes struck a late winner at Turf Moor on Saturday.
Spurs felt the corner from which Chris Wood headed the opening goal was incorrectly awarded and Lloris raged at the decision in a post-match interview.
"For me it was obvious. It is the responsibility of the referee," Lloris told Sky Sports . "Then it is our responsibility not to concede from the corner.
"It is not the first time that type of thing has happened with the same referee, but it is not my position to talk about that."
"Obviously it is a big disappointment," the France goalkeeper added. "Today was a good opportunity for us and we missed it. It was a tough game. We expected a battle.
"We were in the game. We had a good fight and it was difficult to keep the ball on the floor because the pitch was dry and windy.
"We conceded the first goal and it makes things harder. Especially when you concede a corner that didn't exist. It is part of the game.
"It was an open game when we scored. Unfortunately we didn't get the result that we wanted."
4 – Ashley Barnes has scored in each of his last four Premier League games (4 goals), after netting in just three of his previous 24 in the competition (4 goals). Bundle. #BURTOT pic.twitter.com/BgIUY5G3Yq— OptaJoe (@OptaJoe) February 23, 2019
Sean Dyche's team are unbeaten in eight Premier League games after beating Spurs and the Clarets boss hailed his side's victory.
"It was a thorough performance and a good win," he told BBC Sport.
"We know there's a lot of work to be done but they're certainly putting in the work.
"We're not a side who can slick it around like Man City, but we have very good players.
"We wanted to get in behind them. I thought our front two [Barnes and Wood] were outstanding."