Rodgers praised his youngsters for getting Liverpool out of trouble after another nervous, error-rich showing from his side.
The Anfield boss admitted his team made too many mistakes as they allowed Middlesbrough come back from behind on two occasions and forced a tense penalty shoot-out which took 30 penalties to decide the tie.
After watching his team convert 14 out of 15 penalty kicks, Rodgers felt the night offered experience and confidence to his rising stars like Jordan Rossiter and Jordan Williams.
But he also showed concerns over the number of errors made during the match.
“I just felt we are making mistakes, too many mistakes and we are being punished for them,” he admitted. “I was disappointed with the first goal, and even more with the second, to give the ball away sloppily like that, and lead to a penalty was really disappointing.
“We haven’t started great this season, but we are still finding our form, and it’s a good night to get through.”
The manager believes his centre backs Manado Sakho and Kolo Toure – who both mistakes that allowed boro equalise – have the youngsters to thank for saving their skins.
“We showed great resilience and mentality to keep going, and at the end we showed great composure from some of the young players to get through that,” he added.
“Tonight was a good night for our young players.
“Young Jordan Rossiter, I’m delighted for him. He could almost walk to the Anfield Stadium as he lives round the corner. It was a wonderful finish, and again great composure.
“Young Jordan Williams too, did really well, he was bright and strong for us when he came on, and it was great for the spirit of the team, I’m really happy for them.
“It’s an opportunity for them. It shows the youngsters in the academy that we want to try and grow them here, otherwise there’s no point in having a youth academy.”
While Rodgers was a relieved man, Boro boss Aitor Karanka insisted he was proud of his players – especially as they exposed the weakness in the home defence.
He revealed that he knew they would score goals at Anfield and he said he retained hope, even when extra time was drawing down with the Reds leading:
“I told the players before the game if we were organised we could make problems for Liverpool, because they were not in good form with the last two defeats in the league, and yes, we gave them problems.
“It’s difficult when you play at Anfield with the crowd, but I even told the substitutes when they went on we would have chances to score – and we did.
“I felt we could create chances because we knew we could take advantage of the spaces they left, and we have very good players in front who can score the goals from those spaces.”