In his 100th game in charge of Spurs, Pochettino made seven changes to the side from Saturday's Premier League draw with Arsenal, with striker Harry Kane on the bench, while Eric Dier and Danny Rose were left out of the squad.
The Argentine's decision to rotate backfired as Dortmund dominated the last-16 encounter and head into the second leg at White Hart Lane next week with a comfortable lead courtesy of goals from Marco Reus (2) and Pierre-Emerick Aubameyang.
"No regrets. I'm very disappointed with the result but we didn't have a very good day. It was a bad day in the office," Pochettino told reporters after the game.
"When we analysed the squad and picked the starting eleven, we tried to win the game. It started okay but it was a really bad day for us."
Spurs, who are second in the league, five points behind Leicester City with nine games left, will look to get back to winning ways when they travel to face bottom-side Aston Villa on Sunday.
"I am not worried, I know the circumstances. We need to accept some periods during 10 months that we will have good and bad times. We have always had things good," Pochettino added.
"We have a big challenge against Aston Villa on Sunday. We are in a very good position in the league and we will do our best."