Spurs beat the Saints 3-2 in their fourth round replay and will now host Norwich for a place in the quarter finals.
Heung-min Son’s 87th penalty ensured Tottenham progressed though Mourinho was forced into changes from the impressive win over Manchester City at the weekend.
Steven Bergwijn and Erik Lamela were among the players not available to Mourinho and the boss lamented the amount of injuries he is facing at the moment.
Mourinho said: “We’ve a very small group of players with so many problems we’re having, and everyone is giving absolutely everything.
“To lose after giving so much would have been painful. I’m so happy for them. They were phenomenal.
“The way they reacted was fantastic, showed incredible heart and connection with the crowd. I think the best team lost - but we deserved to win.
“I cannot speak about the progress I want to make because I don’t have the players I want.
“And the team needs players to progress, collectively, tactically and dynamically. We need the players but we don’t have the players.
“We lose so many. Sissoko, Harry, and today Lamela, Lo Celso and Bergwijn. It is so difficult.
“One game we have players A, B and C out and then the next game we are without D, E and F. It’s been a very difficult season.
“Do we progress by the mental point of view? Yes. Do we progress by the competitive point of view? Yes. Do we improve the compactness of the team? Yes.
“Do we improve from a tactical point of view? No because one day we play with five and the next day we have to play with four. I couldn't even play with three up, I only had two!
“So we come from a game against City when we played with three up but we came here and had only two. I don’t know if we will have one for the next game. I don't know if Lucas and Son are going to finish. I don’t know.
“So it’s very difficult to progress the way we want to. It’s more like, let’s build a team to compete in the next match.
“Basically it’s game to game, building a team with what we have to try to get a result. And the players are being magnificent.”
Mourinho will be hoping he has more players available for Tottenham’s next match with Spurs heading to Aston Villa on February 16.