Spurs narrowly failed to make a successful defence of the trophy at Wembley on Sunday after losing 4-1 on penalties after a 0-0 draw.
The Premier League strugglers matched their opponents before the shoot-out and Jenas was happy with the performance.
However, with Middlesbrough visiting White Hart Lane in the league on Wednesday, the midfielder concedes Spurs must quickly pick themselves up.
Heartbreaking"It's physically and mentally draining, and when you don't win it's heartbreaking," said Jenas.
"You go through an abundance of emotions, but we have to pick ourselves up. We haven't got time to dwell on this."
Jenas is confident that, if Spurs can replicate their performance against United, the club will be able to move away from the relegation zone.
He added: "We can take a lot out of it, there was a lot of courage and effort, and if we put that in from now until the end of the season then we'll climb the league.
"We haven't got time to think about it. Regardless of if we won or lost, we have a very important game on Wednesday that we have to focus on.
"We have to recover as much as we can and make sure we are ready for Wednesday."