Head coach Tom Shaw said: “It wasn't a great day at the office. It was a disappointing performance.
“We just didn't seem mentally ready at the start. I want to see the lads' eyeballs bulging out their heads at the start of a game. When they're like that we're a difficult team to play against.
“Lancaster are what they are and they are good at it. They don't really take more than one touch and it comes straight back at you. We let it happen too easily early on.
“The whole team has to defend better.
“We managed to get to 1-1 with a brilliant goal – a bit of a get out of jail for us I thought.
“We started the second half well but just didn't carry enough of a threat.”
He added: “It looked like going to penalties as I don't think either team did enough to win a poor game of football.
“But they scored, we are out and we have to learn from it pretty quickly and take the medicine. It was a winnable game for us.”
Trinity now head for third-place South Shields on Saturday and Shaw said: “Playing South Shields away and starting a game like last weekend, we'd be in real trouble.
“The outside world will think we'd struggle to get anything from the game this Saturday so the belief has to come from within us.
“We need to dust ourselves down and stick together and we will be fine.”
Trinity were punished for a sluggish start on eight minutes as Sam Bailey crossed from the right and Paul Dawson buried a free header.
Two minutes into stoppage time at the end of the first half, Toby Gould was fouled 25 yards from goal, and Brad Grayson curled home a sublime finish into the top right hand corner.
But in injury time, late Lancaster substitute Brandon Lonsdale stole a winner, finishing off a tidy team move down the visitors' left.