However, Barca pounced on a very rare Chelsea mistake on the night as Andres Iniesta intercepted a slack pass by Andreas Christensen and squared for Lionel Messi to slot home his first goal in nine appearances against Chelsea.
The Blues won the Premier League under Conte last season but for much of this term he has faced questions about his long-term future with Chelsea.
According to them, the England worldwide did not feature against Barca because he was "too affected" by the news that Ryan Mason had retired from football. "Playing in front of our fans, on our pitch".
The centre-back was quick to respond on Twitter, writing: "Devastated to hear today's news from Ryan".
"He is only 21 and it is great he can play with that maturity".
"It's very hard to tell one or another player, but I think Christensen played a top game". But if we go with the same mentality as we did against Atletico, we can go there with great spirit and win the game.
And Fabregas feels Chelsea will have no hope of progression if they go to Camp Nou and attempt to sit back for the entire match.
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"When you play against Barcelona you know very well that if you want to face them box-to-box then you are insane and you go to lose the game, not 1-0, (but) 4, 5, 6-0", said Conte.
"It is still open and we have showed we can compete and we will need another excellent performance at the Nou Camp to go through", said Willian, who hit the woodwork twice in the first half.
Despite his record against Chelsea, and the approach of his 31st birthday in June, he looked like Barcelona's most likely route to goal at Stamford Bridge, finding space in Chelsea's otherwise disciplined defence and linking up dangerously with Iniesta on several occasions before the pair worked the equaliser. "The goal will give us a huge advantage in the second leg and allow us to have more space in the Nou Camp", the Uruguayan said. We are talking about Barcelona.
"We were good, we played very well but we made a mistake and then we suffered a goal - but we can go to Barcelona and do a good job again".
Barca midfielder Ivan Rakitic compared Chelsea's tactics to a handball team, huddled around the edge of their area.
Chelsea will travel to face Barca in the second leg of the tie on Wednesday, March 14.
"It's a pity about the draw and there are regrets, because because when you play against a side like Barcelona, you need the flawless performance to win", Conte said.