"I briefly asked myself if we shouldn't withdraw completely from the competition, but that would have been a victory for those responsible for the attack," he told Saturday's Der Spiegel magazine.
The Bundesliga club eventually played their quarter-final first leg tie against Monaco 24 hours later on Wednesday.
The attack on the bus as it made its way from Dortmund's hotel to the stadium injured Spanish international Marc Bartra and a policeman.
Visibly shaken, Dortmund succumbed 3-2 to Monaco, leaving them with an uphill struggle to qualify for the semi-finals in the return leg in Monte Carlo next week.
Watzke revealed that he had left each player with the choice of whether to play or not.
"I said if someone doesn't feel in a state to play he should tell the coach. We would have completely understood and we would have offered every support possible."
Several players strongly criticised the decision to let the game go ahead so quickly after the attack, but none refused to play.
Dortmund take to the pitch on Saturday in the Bundesliga as German prosecutors examine a third claim of responsibility for the blasts, it was reported, although no new suspects have emerged.
Three bombs containing pieces of metal detonated minutes after the bus left the team's hotel.
Dortmund defender Bartra, 26, was hurt by flying glass and had to undergo a wrist operation, forcing him out of action for four weeks.