They had fallen behind when David Luiz gave away a penalty for Antoine Griezmann to score, but Eden Hazard crossed for Alvaro Morata to deservedly level.
And substitute Michy Batshuayi, the man whose goal won Chelsea the title in May at West Bromwich, struck again in injury time, slotting in from close range from Marcos Alonso’s pass.
Conte said: “It was a good performance by my players. I am very happy. We must be pleased with the personality and spirit we showed.
“We came here and showed we were ready to play. We were positive.
“Going 1-0 down as you know its very difficult to come back against a team like Atletico – but we deserved to win. We kept our heads.
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“The personality that we showed was key. Whether you play away or home it does not change – you must play with the same personality and desire. Last season we did that very well. The Champions League is a great competition and we want to be competitive.”
But Conte was not pleased that his team now face a massive game against Manchester City on Saturday – with 24 hours less preparation for the game than Pep Guardiola’s team, who played on Tuesday.
Conte said: “We are a bit penalised. Its very important before taking this decision to analyse the different situations of the teams. City played on Tuesday at home, we played tonight away and for side we will return to London at 4am and to have only one day to prepare for this type of game. It is not right.”
Hazard said: “We are very happy. It was a tough game against one of the biggest teams in Europe. We deserved to win.
“Michy scores every time he gets on the pitch. I am very happy for him.”