The hosts had to mount a nerve-wracking rearguard action in the closing minutes, after Ross Broadfoot's late try and conversion, to chalk up the win which puts them top of the table by virtue of more games won.
Bath's tries were spectacular length-of-the-field efforts, the first from Michael Stephenson and the second finished off by Matt Banahan just after half-time.
"It's a good place for a team to be," said Meehan. "We should acknowledge it and enjoy it. These guys have worked very hard. We are not rapt with the performance today but we got the result we wanted."
He added: "The players know they have to deliver now - train hard and play well in the matches. The younger players especially are getting more experienced and getting used to the speed of the Premiership and its physicality.
"I was delighted to see a couple of younger guys in the squad seeing opportunities and taking them. Matt Banahan's try was what we are striving for."
Meehan raised the prospect of South African World Cup-winning fly-half Butch James being back in action soon.
"We are hopeful that he will be available for the match against Leeds in the European Challenge Cup in a fortnight. But if the physios deem another week is necessary or even two then so be it."
London Irish forwards coach, Toby Flood, admitted that a top-four place was a forlorn hope after they had to be content with a losing bonus point.
He said: "I imagine it's mathematically possible to get into the top four but whether it's really achievable is another matter. We will shift our attention now to getting a Heineken Cup qualification place.
"It was a tight game - we knew it would be. We created chances but didn't capitalise on them. In this very competitive championship, if you don't kick your goals you get punished.
"The Bath boys said to me afterwards that they found it rather fatiguing. If I'm honest, for the second week running we played well with the lions' share of possession but came up short."