The Rams never looked back after opening the scoring through Martyn Waghorn, with Florian Jozefzoon doubling the lead before the break. The visitors remained in control of the tie after the restart and ran out comfortable winners when Brandon Fleming turned into his own net and Mason Mount added a late fourth for Frank Lampard’s men.
“It was a tough night for everyone involved,” admitted Keane.
“We went into the game with plenty of confidence after the Sheffield United game in the previous round.
“We believed we could put in a performance worthy of progressing to the next round against what was a very good Derby County side. However, everyone was a bit deflated with the performance we went on to produce.
“We didn’t impose ourselves the game whatsoever and before we knew it we found ourselves two goals down and chasing the game.
“We need to look at the problems we’re having and sort them out. We can’t shy away from that because we can’t be conceding four goals at home whatever the competition. The fans deserve better than that.
“It wasn’t good enough and we know that we have to better in both boxes if we want to win games.”
Nigel Adkins’ side must pick themselves up quickly before hosting the Rams again in the Championship at the weekend and Keane has called on the Tigers to produce a positive – and immediate – response.
“As I say, it was a tough experience but one we have to take on the chin and move on,” he added.
“We’ll analyse Tuesday night’s game and look at where we have to improve. We’ve got to bounce back and produce a response at the first time of asking on Saturday.
“We know Derby will come here with confidence after their recent results. They’re an experienced side with quality in all areas of the pitch, but we know we have to put things right after our last two displays and give the fans something to be positive about and to shout about.
“We need to put more points on the board and in order to achieve that we need to see an improvement in our performances.”