Johnson struck the only goal of the night against Manchester United in Bilbao.
He said: "I'm so happy right now. This season has not been good at all, not one of us players care about that now. This club has not won a trophy for 17 years, it means so much.
"All the fans get battered, we get battered for not winning a trophy. We had to get the first one, I'm so happy. Ever since I came here it has been 'Tottenham, good team but can't get it done', but we got it done.
"I knew I touched it a bit (for the goal), but not clean, then I looked up and the ball was trickling in the goal."
"(In the last five minutes) I couldn't watch. I was just asking 'how long left?' When we defended that corner, I was getting told it was done and the relief is something I can't describe."
"I can't thank the manager enough"
Johnson also said: "Tottenham Hotspur being 17th in the Premier League is not good enough. We had an unbelievable Europa run. The fans have been so good, home and away and they had the edge over the United fans. They were all here an hour before the game, they got us through the game."
On manager Ange Postecoglou, he added: "He has done his job. He said he wins in the second year and he has, if there's ever a time for a mic drop, it's now (when he speaks to the media).
"I can't thank the manager enough for how much trust he has in us and he has a really good way of getting us up for it."