The Parkhead club are now one way away from the treble after defeating Rangers 2-0 at Hampden. Callum McGregor opened the scoring before Scott Sinclair doubled the advantage from the penalty spot.
Caixinha watched on as Rangers were dominated in the opening 45 minutes and responded with two changes at half-time as Joe Garner and Andy Halliday made way for Barrie McKay and Joe Dodoo.
Rangers were improved after the break but they never looked like clawing back the deficit after Celtic extended their lead through Sinclair’s penalty.
Afterwards, the Rangers boss admitted his team had been second best on the day.
Caixinha said: “I think it was a flat performance for us in the second half - especially in the first half, we could not stop Celtic.
“Not that they arrived down there (at our goal) with too many clear chances but especially because they control and manage all the game in the way they want it.
“In the second half, the key (point) from the game is that we conceded so early. Unfortunately the penalty changed everything.
“We kept trying to look for it (a goal) because at 2-0 the result, if you score you can get a gain on the game (but) we could not and I think they deserved to win.”