"Over both games we have the feeling that everything that could go wrong went wrong," he said.
The kickoff was delayed by five minutes after the German team arrived late at the Louis-II stadium due to traffic problems.
The incident occurred a week after the first leg was postponed by 24 hours after the Borussia team bus was attacked with explosives on its way to the stadium.
Monaco made a fast start.
Benjamin Mendy's fierce 25-metre strike was parried by Roman Burki into the path of Mbappe, who coolly slotted home to put the hosts ahead.
Monaco doubled their tally three minutes later as Falcao perfectly timed his header to beat Burki from Thomas Lemar's cross from the left.
That left Dortmund with three goals to score to force extra time and Tuchel replaced midfielder Erik Durm with forward Ousmane Dembele.
The German side looked transformed after the break and they were quickly rewarded as Reus reduced the arrears when he volleyed home from Dembele's cross after a dazzling run by the Frenchman.
Monaco, however, had a golden chance to wrap up their qualification shortly after the hour but Falcao's chip went over the bar.
Germain replaced Mbappe and had an immediate impact as he latched on to Lemar's cross to score seconds after coming on.
Monaco coach Leonardo Jardim promised his team would stay true to their offensive style in the semi-finals.
"Our rivals will want to draw us (on Friday) but our ambition is to enjoy it and play with our attacking qualities like we always do." he said.
"Tonight we played a very solid game, we were in control but we showed ambition. We were always looking for the extra goal, that is the way we play, it is in our DNA."