Boro ended the Seagulls' remarkable club record run of 22 league matches undefeated since the end of last season with a 3-0 win in the top-of-the-table clash at the Amex Stadium.
First-half goals from Kike and Albert Adomah put Boro on their way to their eighth win in the last 10 league games, and leading scorer Cristhian Stuani sealed the victory midway through the second half with his ninth goal of the season.
Karanka said he chose not to tell his players that Mourinho, sacked by Chelsea this week, was in attendance but was delighted to have the support of his close friend, the pair having worked together for three years when Karanka was his assistant at Real Madrid.
Karanka said: "Jose brought us luck. We worked together at Real Madrid and it was an amazing experience.
"He is a friend of mine. I didn't tell the players that he would be watching but it wasn't a secret.
"Afterwards, he came into the dressing room to offer congratulations. He felt he had watched a really good team and he was impressed with us. He was the best and he will be the best."
Karanka did not rate this as his side's best win of the season, but praised the way they "controlled the game".
He said: "It wasn't our best performance but we have beaten a team who were unbeaten.
"To score the first goal was very important and I'd liked to have scored again before our second goal arrived."
Boro, who now boast six successive clean sheets in the league, are now three points above Brighton and Karanka said his side's aim is simply to achieve promotion.
He added: "We have to keep going. A lot of teams are behind us and they want to be in the same position as us."
Brighton manager Chris Hughton admitted that playing two tough away games in a week coupled with injury problems had played a part in the defeat.
He said: "Middlesbrough looked better than us. We've had two tough away games, had injuries as well and goals can change a game.
"Middlesbrough got an early goal and an early lift. We've now conceded four goals from corners in our last three games and that is something that needs to be eradicated.
"But we were up against a very good side and it's very difficult to be too harsh on the players.
"The reaction from our supporters at the end was excellent, and I hope the impact is positive and this defeat is a little bit of a reality check that allows us to get back to winning ways."
Hughton said he was able to have a word with Mourinho in a brief one-to-one chat afterwards.
The Albion boss said: "He came in to see me which was very nice of him. He was here because of his association with the Middlesbrough manager.
"Time was short but he spoke about our run; he knows the Championship very well. I wished him all the best and look forward to seeing him back in management."