Goals from Aron Gunnarsson and Joe Ralls won three points for Cardiff at The City Ground as the Bluebirds made it seven points collected in the three games since Warnock took over. The late goal scored by 10 man Forest caused some concern but City held out for a deserved victory.
"Nottingham Forest are a good side with some very good players. I was hoping for a clean sheet, but once again we've let ourselves down at the death," said Warnock.
"It was a game we should have won comfortably. I said to Blackie (Kevin Blackwell), my assistant, with five minutes to go that something's going to happen here, because it's too straightforward.
"I thought it was a soft penalty.
"I think Andy (Woolmer), who is a good referee, just got a bit bored and just wanted to make it a bit more exciting for the last few minutes. I wish we had him every week, I think he's one of the top referees. He talks to you, you can understand him."
Warnock added: "I've been asked about promotion. But I just said, 'Let's get out the bottom three first'. We just get carried away, don't we?
"We're nowhere near the finished article, but we've got a good bunch of players and the fans get behind us."
Forest head coach Philippe Montanier, on the other hand, was left to rue individual defensive errors which saw his team slip to a second successive defeat and drop further down the table.
Forest have yet to keep a clean sheet so far this season and have leaked goals.
Cardiff's first saw Gunnarsson score with a free header from a Peter Whittingham corner, while the home team looked all at sea for the second.
"It was a poor, poor result," said the Frenchman. "It's always the same story. We had a repeat of individual mistakes.
"We started well, but then we conceded a goal from a set-piece.
"At 1-0 you can come back, but then we had another mistake.
"It's never the same player making the individual mistake.
"At 2-0, it is difficult to come back.
"We never gave up, even when we went down to 10 men, and we scored at the end, but we keep making individual mistakes."
Montanier had no complaints about Lam's sending off, with the defender given a straight red card for dragging down Anthony Pilkington as he looked to break through.
"It's the rule," he said.
"If your opponent has the opportunity to score and you make a foul, it's a sending off.
"We can't have any excuses. We can't blame the referee or the sending off."