O'Hara saw his spot kick saved by United goalkeeper Ben Foster and then left the pitch in tears, but Redknapp insisted he was impressed with the 23-year-old and that as a club they will move on.
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"He's got a great left foot and was the first to volunteer for one," Redknapp said.
"He left here in tears last year. He feels for the club and is part of the club. I've been impressed with him as a player and a person. I was pleased that he played a part.
"It was a poor penalty for a player who can strike a ball as well as he can but that's one of those things. He had the bottle to take it but unfortunately didn't score."
Redknapp also conceded that despite being more than impressed with his side's performance, he had not asked his them specifically to practice penalties before the final.
"I thought we were terrific. It was a great performance. It comes down to a lottery in the end with penalties," he told Sky Sports
"I have to be honest, we were not that confident with our penalty takers really and you looked over there and they had very confident penalty takers. But overall they couldn't beat us in 90 minutes plus extra-time.
"We fought them. I thought we didn't deserve to lose today. I thought we were better."
Meanwhile, midfielder Jermaine Jenas wants Tottenham to take the spirit their Carling Cup performance into their survival bid, insisting there is no time to dwell on the defeat.
The White Hart Lane outfit are just two points above the relegation zone and the focus must now shift back to Premier League survival.
Insisting his team mates must avoid lamenting the loss Jenas said: ""It's physically and mentally draining and when you don't win it's heartbreaking," Jenas said. "You go through an abundance of emotions but we have to pick ourselves. We haven't got time to dwell on this.
"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 that 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."