The Biancocelesti ended their opponents' 12-game winning run in Serie A on Saturday.
"We had a terrible start, as for 20 minutes we were slightly nervous under their pressing. We did better, were a little unlucky to hit the woodwork twice, as we could've won," Reja told Sky Sport Italia.
"The team reacted very well, Klose had two or three good chances and I had hoped we would win. Juventus by-passed the midfield and started to float balls in for Llorente which were very dangerous.
"Juve are very talented and at a very high level, so it was not easy even against 10 men. We knew that we could have difficulties in the middle and defending on Carlos Tevez and Llorente, so we used a three-man defence and did well to close down their trajectories in the middle. Perhaps we should've done better on the counter-attack. Marco Storari also performed some extraordinary saves."
Lazio visit Napoli in the Coppa Italia on Wednesday.