The former Charlton defender admitted that the potential lure of European football was one of the decisive factors in his move.
"I saw the game on Tuesday night but I had no doubts about having signed," said Bougherra.
"When you come here you know that Rangers will play every season in Europe, and it's a dream for the players.
"I was very disappointed sitting in my room. It was raining, and I didn't feel good.
"Afterwards it was brighter and I thought 'My contract is four years' - and we will win the championship and there will be no worries.
"Of course, European football was a big reason for me coming here.
"I saw the Uefa Cup final last year and I knew that there would be the chance of Champions League football every year, so it was a dream.
"I want to play in the Champions League next year. But I can wait for Europe - it's no problem. I am 25, so I have time to play in Europe.
"I never thought I had made a mistake. It was frustrating watching Rangers go out. But now it's behind us, and we're concentrating on the league and we want to win trophies."