Cole has a contract until the end of the season with the play-off-chasing Championship club, but Lampard sees no reason why his former team-mate cannot extend his professional career.

Asked if he can see Cole playing another FA Cup match, Lampard said: "Maybe, maybe. He's been a machine all of his career in terms of fitness and looking after himself – if you look at him, he's as lean as anybody.

"And as long as he has the desire, then that's his call.

"I'm delighted for him because, at 38, he could comfortably kick back probably now already.

"I thought he was calm and assured on the ball, as we know, he's obviously got all the experience of his career and then he got his goal, so really good for us and we'll need him.

"He has a real desire and a humility and a work ethic and I think his performance was good and it will get better because of fitness.

"Now we have a player who is ready to start games."

Derby left themselves with too much to do on the south coast after first-half goals from Anthony Knockaert and Jurgen Locadia put the hosts in control.

Cole's close-range header made the home fans sweat but, despite four minutes of stoppage time, the Rams could not force extra-time.

Lampard admitted his team had paid for their poor performance in the opening 45 minutes, which left them with "a small mountain to climb".

"First half we were slow, lack of urgency. To come to a Premier League team and give them time on the ball is a cardinal sin," said Lampard.

"We weren't at the races. Whether it's fear, whether it's respect, it's not enough to come here to get a result.

"That performance in the first half cannot get you a result. The second-half performance can but it was difficult because we had a small mountain to climb."

Victory for Brighton puts them into the quarter-finals for the second successive season and provides a welcome distraction from their top-flight relegation battle.

Mali international Yves Bissouma, a £15million summer signing from Lille, inspired the win by helping to create both goals.

And Brighton boss Chris Hughton was impressed by the midfielder.

"He's a very talented young player that's still adjusting to the game here and the competitiveness of the game here," said Hughton.

"I thought today he was very good.

"He showed his quality, great participation in the goals that we scored and these games will all be good for him."

Hughton also felt his team should have enjoyed a more comfortable afternoon.

"Very nervy at the end and probably the only disappointment that I have got is I thought we made harder work of it at the end than we needed to," he added.

"But I thought for the bulk of the game, we were fairly good."

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