The Championship play-off winners found themselves 4-1 down in the second half as Leeds took full control, before Parker's men fought back to score twice more and make it a more tense affair.
It means Fulham have lost both their opening Premier League games and already have a goal difference of minus six.
Parker did find reasons for optimism in his team's performance but was chiefly focused on what cost them the game.
"Frustrated," he said.
"Overall you can't expect to score four or five goals to get something out of a game, thats what we've had to do today. Of course there were positives, I really liked us in possession, we caused Leeds a lot of problems. On the flip side you give away easy goals you give yourself a mountain to climb. The biggest thought in the front of my mind is exactly that. We need to improve there for sure. It was an entertaining game, we were largely to do with that. We showed character, at 4-1 the floodgates could have opened. We probably gave ourselves too much to do."
Parker believes his side need to have a different mindset when it comes to defending or they will continue to get punished in the top flight.
"We all realise that, I certainly realise that," he said.
"You can't give goals up as easily as we've given them up. We need to understand that. For me it's not about a training, showing certain aspects, work all week, it's about a mindset when it comes to defending, a bulb that goes off in your head. There are critical moments when you have to be on high alert. In the Premier League at any given moment, if you can't sense that danger then you're going to struggle. Of course there's individual mistakes but the biggest issue for me is that at certain moments you need to show a different side to you. At times we're too nice. Within split seconds the ball is in the back of your net from something you don't see coming."
He vowed that the character the team showed in coming back from three goals down to make it a one-goal game will remain on show this season.
"There's massive hope, that will always be there," he said.
"This team and my team will fight all year. We'll do everything in our power to try make this year successful. We realise we're in the best league in the world, we'll come back fighting again. We're going to have to learn, try improve things, either with different personnel.
It's a massive positive [coming back to 4-3 from 4-1] against a team that gave the champions a real tough game. For large parts we had a lot of domination. We can't be weak in the other side of the football match and we were today."