The Bundesliga club's team bus was stopped by police for 20 minutes as it was making its way to the Stade Louis II on Wednesday, forcing the quarter-final second leg's kickoff back by five minutes.
"The bus was supposed to depart at 7.15pm. Everyone was on the bus and the police were ready to accompany us, but then we were told we had to wait," Tuchel told Sky Sports News.
"We stayed there for 16 or 17 minutes and when we tried to find out why, they just said it was for security reasons. It was the worst thing that could happen a week after the attack, everyone was on the bus ready to go but we were not allowed to.
"You come into such a game trying to have a clear mind to go out and turn the tie around, but with just an hour and a quarter to go before the match, we were not able to think about football at all and it wasn't ideal."
The result on the night meant that Dortmund were knocked out of the Champions League 6-3 on aggregate.