The county were beaten by an innings and 62 runs by Worcestershire at New Road, meaning they have lost all three of their opening Division One matches.
"I'm a little bit shell-shocked," Trescothick, 39, told BBC Somerset.
"We haven't performed anywhere near the level we expect as a team. We've been slightly off the boil."
Somerset began their season with a seven-wicket defeat by Durham at Taunton, before losing by five wickets against Middlesex in their second match, despite first-innings centuries from Trescothick and James Hildreth.
They now face a four-day game against New Zealand, starting on Friday, and resume their championship campaign against Nottinghamshire at Trent Bridge on 17 May.
The County Ground outfit, who have never won the County Championship title, finished sixth in Division One last season.
"We've got some soul-searching to do," said former England batsman Trescothick. "We can't carry on in this vain because it's just not good enough.
"I don't think I've ever lost three on the bounce in a championship season. It's new territory for us to think how we're going to recover from this point.
"There's areas for us in quite a few departments we can improve upon.
"This is where your team unity and all the work you do behind the scenes has to come forward.
"At the end of the day, it's about players putting their hands up and putting performances in. That's the challenge for all of us going forward."
Somerset need to do some "soul-searching" after their third County Championship defeat in a row, says captain Marcus Trescothick.