The Warriors returned after the interval with far greater intent but were unable to make up the 20-point deficit.
In a highly-strung encounter, Glasgow also lost a player to the sin-bin either side of half-time; first Tom Ryder for killing the ball and then DTH van der Merwe for striking Aled Brew.
"The guys didn't front up in the first half and the Dragons had a little bit more desire after last week's game, you could see that," said Lineen, who led the Warriors to an inaugural Play-Off spot last season.
"We just got bullied again, but I have to say for a team to get bullied and get yellow carded twice showed we lacked smartness as well. It was really frustrating as there was a lot of grabbing and pulling and we reacted. All week we said concentrate on the game and we didn't, not until it was too late.
"It was an appalling first half. We got bullied up front, there was no direction, we were too slow to clear the ball, nobody wanted the ball and we waited to see what they had. We knew the first 20 was going to be really important, whether playing into the wind affected the side I don't know, but there was just no spark.
"There are no excuses, absolutely none, the lads are better than that. It's part of the learning curve, there were a lot of youngsters out there and we just didn't front up."
Glasgow couldn't cut free from the Dragons on Sunday
After some stern words at half-time the Warriors put in a far more committed display but, despite their dominance during large periods, the Dragons' defence held strong. Only Richie Gray crossed for a try before a second Ruaridh Jackson penalty signaled the end of the scoring.
"In the second half we got a few guys on and the two Richie's (Vernon and Gray) stood up. But any time we got momentum something happened. We lost DTH for 10 minutes which was ridiculous after he got taken off the ball and then spear tackled," added Lineen.
"When you play the Dragons you play the game for the game and you have to play that game pretty well and keep your discipline. Again it comes back to two yellow cards - it's incredibly frustrating.
"We didn't have the control in the first half, we didn't have the platform and we made some poor decisions which didn't get us into the game. To be down 23-3 at halftime was really frustrating, we just gave them too much. In the second half the boys just did what they were meant to do but we just didn't do it often enough."
Glasgow arrived in Newport on the back of a morale-boosting win over Leinster at Firhill on the opening weekend but were unable to match that intensity at Rodney Parade.
Instead, the Warriors were out-fought by their Welsh opponents as they slipped to eighth-place in the Magners League standings ahead of Friday's home clash with Connacht.
"A lot of guys are disappointed with the overall performance but it was only the second game of the season and a lot of the lads will learn from that. It was a real lesson for Henry Pyrgos at scrum-half - okay, the forwards didn't help him much but he was given a torrid time in the first half.
"The guys need to realise we came down here to win a game, it's not about just turning up after saying nice things in the week after a great win - you have to forget about that. This is a tough place to come and get a result. We knew Aled Brew was dangerous, he is a quality performer and you have to be careful with him, you don't let him play on the counter attack.
"But it's just ultimately disappointing for the players. They have worked hard, we've worked bloody hard and we just gave up. The players know that themselves."
63x46.png){kind=logo}