The Denmark midfielder struck in the 54th minute to continue their unbeaten start to the season with a 1-0 triumph at Cardiff.
The victory saw Bournemouth leapfrog Fulham into top spot, and Parker believes the 25-year-old has grown into a key player for his side.
"I am delighted for Phil," said Parker. "We have been working hard on his game and there are unseen aspects that are now working very well. He has matured.
"In the past, I saw a player who could float in and out of games and maybe could go missing at times.
"Now, I think he is superb. We know what you get with him technically, but he also now ticks all the boxes when it comes to his defensive work and his understanding of the team dynamics.
"This was a massive result and it brought to an end a huge week for us with three wins. I thought we were superb today and looked every bit a top side.
"We were up against a big, physical side who deliver long throws and who can cause you massive problems. I asked my players to be brave and they were."
Bournemouth dominated 72 per cent of possession but failed to break through the Cardiff defence in the opening 45 minutes.
The decision hit the Bluebirds boss even harder two minutes later when the visitors made the pressure pay through midfielder Billing.
"I've just seen the Lerma tackle and I've told the ref to have a look at it," said McCarthy.
"It's a red card in my mind, he's gone over the ball and when they see that on the video they will agree with me.
"The referee made his decision, I'm not complaining, we all get things wrong, but it's not easy when you concede afterwards.
"They are an almost perfect Championship team, they're athletic and they have good footballers, they're big and powerful and they can play so it was always going to be a tough one for us.
"For 55 minutes I was delighted with how we set up to frustrate them. We blinked once, they played through us and we've been done.
"But in fairness to the lads, they kept going and fought until the end which I can't fault.
"Our only problem is that even though we managed to stop them, we created very little until the end of the game."