Abraham tapped home the only goal of the fifth-round tie with the visitors’ first shot on target in the 64th minute to set up a quarter-final versus Sheffield United at Stamford Bridge.
But it was Championship side Barnsley who created the better chances.
When asked if he was a relieved man after his side’s below-par display, former Paris Saint-Germain and Borussia Dortmund manager Tuchel said: “I have to be honest, yes.
“We can stop the analysis. What is done is done. Chelsea are through to the quarter-finals.
“We can clearly play better. That’s not our best performance. To cope with the difficulties today, it was hard for us to cope with the [Barnsley] pressure.”
Abraham also rescued Chelsea at the other end soon after he had forced the breakthrough, heading the ball off his own goal-line to keep out Barnsley substitute Michael Sollbauer’s effort.
Tuchel admitted Abraham had made all the difference, adding: “In a story like this clearly, yes. He scores decisive goals in cup games and of course the stop on the line was crucial for us. It’s good for him, because for strikers it’s important to score.”
Barnsley were unlucky not to be in front at half-time after Callum Brittain twice went close to giving the hosts the lead. His close-range shot forced a superb reaction save from Kepa Arrizabalaga and another goalbound effort was deflected wide.
Barnsley boss Valerien Ismael insisted his side achieved their main goal, which was to try and match Premier League opposition in all areas.
“We got the result we wanted. The most important thing tonight was the performance, to compete at that level,” he said. “We had a lot of questions before the game. Can we compete at that level? Can we force our principles against Chelsea, who are one of the best teams in the world?
“And we did it. Especially in the first half, we were the best team. We had two big chances to score. We had to score.
“In the second half Chelsea changed their shape and had more control of the game and we had to adapt and we did it well.”
Ismael, who has guided Barnsley from the lower end of the Championship to mid-table since replacing Gerhard Struber last October, said he could not have asked more of his players.
“I’m really proud of the guys,” he added. “They gave everything to raise their game. Their whole performance level was what we needed to compete and they believed.
“They were determined in everything they did and this is what you need if you want to make the next step.”
Discussion about this post