The defender headed home the Glovers’ third of the match and was part of a defence that were solid and resilient for 88 minutes at St James Park.
But a crazy five minutes at the death saw Exeter make an astonishing comeback to salvage an unlikely point.
Lacey admitted the players let a lot of people down and the 23-year-old can’t wait for Town’s next fixture – Carlisle United at Huish Park on Saturday (3pm) – to make amends.
“I don’t think I’ve played in any games like that – it’s a wake-up call,” he told YTFC’s official YouTube channel.
“We played so well for 88 minutes and soon as one goal went in, we ended up losing our structure and standards dropped.
“We ended up letting ourselves, the fans and the manager down. We’re very disappointed and it feels like a loss.
“Our game management (could have been better) and we should have wound down the clock. As soon as they got one we sort of lost our calmness and as soon as their fans got behind them it makes it difficult.
“It just shows we can’t switch off and become complacency when we’re 3-0 up. It’s very frustrating to be up and draw like that.
He continued: “It’s a bitter pill to swallow but we’ll have to learn from it and make sure we’re more rigid in the future.
“We’re looking forward to next Saturday to try and make things right.
“We can only improving by looking at it, seeing where we could have been better and getting a proper diagnosis of it which will be beneficial for everyone.”
Francois Zoko grabbed Town’s first in Devon – his 12th of the season – before youngster Shayon Harrison scored his first goal in professional football.
Lacey praised the duo for their contribution and was happy with his own effort despite it not proving to be the match winner.
“I’ve managed to get a few with my feet so it’s good to add one with my head and hopefully that can continue,” he said.
“It’ll be a massive boost for Shayon. He’s a great talent and I’m sure that’ll be a massive confidence booster.
“Zoko’s always dangerous round the box and when we can get the ball to him he can show some magic.”
Tickets for Town’s match with Carlisle can be purchased in person at the ticket office, online or by phone on 01935 847888.