Parker hailed a “heroic” defensive display which saw the hosts hold out for 78 minutes before Mason Mount earned Frank Lampard’s side a 1-0 win.
And he says he will have to take the rough with the smooth as he demands full commitment from his men in their bid to stay in the top-flight.
“I want every one of my players to play right on the edge,” Parker said. “Be aggressive, and at times when you are on that line individuals might step over that. If that’s the case today then that’s the way it is.
“But without being on the edge, for us this year, we’re not going to be competitive.”
The defeat brought to an end a run of five straight draws in the Premier League and Parker admits he was beginning to believe in his side’s ability to make it six until Mount struck late on.
“You never feel you’ve done enough because of the circumstance of being down to ten men and the quality they have on the pitch,” Parker added. “At that point we knew the game would go 95 minutes, probably.
“But then you get to 70 or 78 minutes and you’re thinking: ‘Can we hold on?’. I think we defended heroically.
“I’ve got nothing but admiration for my team and the way they played.”