Lesley Ugochukwu struck for Burnley, though Villa went onto win thanks to a double from Donyell Malen.
Post-match, Parker said: “I feel like I’m saying the same things again and again. We were competitive again, like we have been all season. But you can’t afford to switch off in this league. One second – and you get punished.
“At times we were hugely competitive but ultimately we switched off and were naive in moments. We lacked a little bit of nous in managing the game.
“That was a flaw for us today and certainly that’s an area we need to fix up on. We just fell a little bit short. I’m frustrated because I feel like we’ve been really close this season in games, as we were again today.
“We only really found our rhythm in the final 15 minutes, but it came a little bit late for us in the end to be honest.”
He also said: “Our endeavour was a huge positive again. There are more huge positives but there’s such fine margins in this division and we’ve found that at our cost this season.
“I’m a rationale guy and perspective is paramount, for sure, but we need to improve in certain areas and that’s something we will endeavour to do.
“The challenge is still in front of us - we’ve been right in games and I’m confident we will keep doing the right things.”