A poor backpass from Michael Essien allowed Jay Rodriguez to give the Saints the ascendency inside the opening minute but the Blues recovered thanks to second-half goals from Gary Cahill, John Terry and Demba Ba, prompting positive praise from Mourinho.
"It was the worst possible start but I think we had the quality to keep balanced and wait for the second half to risk and to try to score a goal," he told Sky Sports.
"We did not lose our balance. We kept calm, even when Oscar had to come out (just before half-time). I played (Frank) Lampard, not Demba.
"We knew that in the second half we could change things and I think the second-half performance was very good. We showed emotion and heart, and quality too.
"I think we gave Southampton something in the second half they were not expecting and they couldn't cope with it."
Mourinho added: "The goal was like a knife in our back; by surprise you are losing 1-0.
"(But) in the first half we played very well. We played with balance, we played calm, no panic, no silly decisions, no mistakes, not going from 1-0 to 2-0, not risking a lot. That was a sign of maturity.
"We deserved the three points in a match which was a must-win for us. We knew that three title contenders lost points before us, so it was important for us to win this game."
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