Full-back Nick Abendanon, wing Joe Maddock, prop Duncan Bell, flanker Michael Lipman and centre Shaun Berne all touched down as Worcester wilted 37-19.
Meehan said: "We must not be scared of going out and playing. We can't go into our shells, even if the ELVs can put you under a lot of pressure.
"I was delighted to see some action in our own 22 today - it was a bit like how we played last season. The rewards of such an approach over the course of a season will outweigh the risks.
"It has taken us the best part of 18 months trying to develop an attacking brand of rugby, and we don't want to go into our shells."
Bath moved into Premiership play-off territory after brushing aside Worcester, making it three wins out of four heading into next Wednesday's Adams Park appointment with champions Wasps.
And Abendanon, capped by England last year but then omitted from their World Cup plans, delivered an eye-catching display that could help thrust him back into Test contention.
Meehan added: "He's working hard on areas of his game that he needs to work on. He is a better pro now than he was.
"I think he is making better decisions with ball in hand, and he is a player who is in good touch."
Worcester scored a late try through wing Chris Pennell, who also kicked a long-range penalty, while fly-half Loki Crichton slotted four penalties, but they had no answer when Bath stepped things up.
Warriors rugby director Mike Ruddock said: "The final score hurts us, as does the fact Bath scored a number of tries.
"We've had some big battles recently against Leicester and Wasps, when we were very competitive.
"We were very competitive for long periods against Bath also, but we had the odd five minutes or so when we dropped our standards.
"Bath have got a lot of pace once they get in behind you. They are very difficult to stop."