Slavisa Jokanovic said he was "satisfied" as Rhian Brewster's first goal for Sheffield United earned the manager his first win in charge.
Brewster scored in the 24th minute, his maiden goal since joining from Liverpool last summer, as the Blades beat Carlisle 1-0 in the EFL Cup.
The visitors rallied late on with Manasse Mampala failing to hit the target with a shot from inside the area and Tristan Abrahams heading over from a good position.
But Jokanovic said: "I have to be satisfied as this is my first victory as manager of this club.
"I cannot say we played a perfect game. A lot of work is ahead of us.
"We have tried using players in different situations tonight. The quality is there.
"It's an important moment for him (Brewster) with his first goal for the club. He can help us a lot this year.
"He showed a lot of desire and tried to do everything he could."
Goalkeeper Aaron Ramsdale was not involved as talk about his future continues, but Jokanovic said: "There is nothing in his absence tonight. I'm giving people a chance tonight and Aaron is my first choice but if something happened I need to be ready."
Carlisle boss Chris Beech was disappointed to head home out of the cup.
He said: "I'm disappointed, to be honest, not to have drawn the game, but we didn't so we're out of the cup.
"They didn't really carve us up and they didn't have too many shots but they scored a good goal in the end and we couldn't get ours.
"It's a great learning curve for the younger ones and they will benefit from the experience. I don't think they were overawed. That was just the way we played to try and contain chances against us.
"We defended well, opened the game out, attacked well and looked like the stronger team finishing the game. That's testament to everybody."
