Liverpool boss Brendan Rodgers was relieved to see his side return to winning ways on Tuesday as they overcame Middlesbrough 14-13 after the penalty shoot-out.
The Reds suffered surprise defeats against Aston Villa and West Ham United in the Premier League but showed grit after Patrick Bamford's last-minute penalty forced a shootout.
"It was very important [to qualify]. You can see how happy the players are," Rodgers told Sky Sports.
"They are competitive players, they want to win in every competition.
"Tonight, a lot of the players haven't played a great deal. Jose Enrique, I thought, was outstanding, he got through the whole game and extra-time and showed good composure on his penalty.
"We're all very happy. We're in the hat for the next round, that's all we want.
"It was a great quality of penalty, I thought both teams showed great composure.
"We're obviously very pleased to get through after being in the lead and giving away poor goals, to be honest.
"At the moment we're making too many mistakes, but I can't fault the character and the mentality of the players because they kept going.
"In the extra period of time, in the 30 minutes, we were very good. We had to step up to get into the next round, we won it on penalties, and congratulations to Middlesbrough, they were excellent and I can see why they are towards the top of the Championship.
"But great for us to get through and a great night for our young players."
17-year-old Jordan Rossiter marked his Liverpool debut with a goal and the manager says he was impressed by the performance of the youngster.
"I thought he was excellent, showed really good composure, his temperament was good and he followed up the finish really well, because it wasn't an easy one, he had to play it through bodies," said Rodgers.
"Young Jordan Williams coming on as well, I thought he showed great stature and presence on the field, was calm on the ball, passed it well and was excellent.
"And young Suso, I must give credit to him because he hasn't had a lot of chances over the course of the season so far, but he came on, he was bright, created his goal and showed good composure in the penalties.
"So, all round, it was a good night."
