Spurs manager Mauricio Pochettino said after the win: "We have respect for Sheffield United - it is never easy. Yesterday they played very well and deserve to be in semi-final. We expect a tough game."
Rodgers, after watching his Liverpool side defeat Bournemouth, said: "It didn't matter who we got in the draw, it was just important to get there - to win this competition you have to win games against big sides.
"I thought it was a brilliant performance from us tonight, it was always going to be a difficult job, but we controlled the game and pressed at the right times and created chances. We thoroughly deserved it.
The semi-finals will be played over two legs, with the first during the week commencing January 19 and the second the week beginning January 26.
The winners of those ties will then meet at the final at Wembley on Sunday March 1.Reuse content