The former Real Madrid defender saw goalkeeper Jason Steele sent off shortly before the interval but was happy with what his side accomplished afterwards in the 2-1 loss at Elland Road and is now convinced they can climb the Sky Bet Championship table
Karanka said: "It would have been better if we had won, but I am happy because we played very well in the second half when we were down to 10 players."
Karanka side-stepped questions about Steele's dismissal for charging out of the penalty area and bringing down Leeds striker Dexter Blackstock.
"I prefer to talk about the team and how we were still in the game until the final whistle," he said.
"I have had just 10 days with the players but they have shown a good attitude and with that we can build.
"Even so, there may be changes for the next game, depending on what I see on the training ground."
Leeds, meanwhile, advanced into a play-off position for the first time since September, with in-form Ross McCormack again on the mark.
McCormack, who took his goal tally for the season to 13 in all competitions, opened the scoring against the club which had three bids for him rejected in August and although Mustapha Carayol equalised seven minutes into the second half, defender Jason Pearce headed Leeds' winner five minutes later.
Leeds manager Brian McDermott said: "We have tried to find a way to play with no wingers and to get Ross up field as much as possible. If he plays right up the pitch he will score goals.
"Every time he plays he looks as if he is going to score. There were bids for him but that is not really relevant because he wanted to stay at Leeds and never wavered."
McDermott added: "Sometimes you are better playing against 11 men. We have found that in the past. It is psychologically harder against 10. We couldn't get that third goal but the result was the most important thing.
"They could have had a man sent off for handball earlier, but I'm glad they didn't go down to nine. It's good to be in the top six but I would rather be even higher. There is much more to come from the team."
McDermott revealed that talks are under way with talented young midfielder Alex Mowatt over a new contract.
Mowatt is growing in stature with every game and McDermott said: "Alex is doing very well for us. Why would he want to go and play anywhere else?"