The Argentine was pleased with how his fellow team-mates dealt with the threat that Tottenham showed, putting their competence down to preparation
The centre-back, 27, played a part as Spurs fought back from a goal down at Estadio da Luz before the hosts' penalty in stoppage-time secured a 2-2 draw for Jorge Jesus' men and kept their 16-month unbeaten record at home intact.
The second leg followed a surprise 3-1 win at White Hart Lane last week and the Argentine insisted that last year's Europa League runners-up did not doubt themselves at any point due to proper planning despite the tough task at hand.
"It was a very physical game, but fortunately we were able to secure a passage into the next stage of the Europa League," Garay told reporters.
"We knew what awaited us was a hard game but we showed that we were prepared for any eventuality."
Benfica are joined in the last eight of the European tournament by Juventus, AZ and Valencia among others, with the quarter-final draw to be held on Friday.