BATH head coach Gary Gold is trying to keep his squad's feet on the ground after a second consecutive bonus-point victory propelled them above west country rivals Exeter and with every prospect of a Heineken Cup qualifying spot next season.
Late tries from Nathan Catt and Anthony Perenise ensured a sixth win in succession for Gold's side, by an ultimately emphatic 40-16 scoreline at the Recreation Ground.
But he said: "I'm really keen to emphasise that I don't want us to get ahead of ourselves.
"We're getting some things right but it wasn't a great first-half performance. There were a couple of opportunities we could have finished so I suppose the exciting part is there is a lot of room to improve.
"The basics are there and the forwards are setting a platform. I hope we are playing an entertaining game and we are scoring tries. Obviously, we are really happy with that as a performance.
"It was a very good Irish team. We had to bring our 'A' game to beat them today. They have a very good backline and we had a lapse of concentration at one point.
"These games are not won at 14 points up and we have to be hard on ourselves to put teams to bed."
Gold said he believed fly-half Stephen Donald had popped a rib cartilage and, if so, the New Zealand international could be out for four weeks or more. Captain Francois Louw, meanwhile, will have a hip injury assessed.
Bath trailed 6-0 early in the game but came back to lead 17-9 at the break, nudging ahead with a penalty try before Nick Abendanon crossed.
Jack Moates was involved twice in the move as he scored a magnificent try for the Exiles but a Tom Heathcote penalty and the two late tries eased Bath to victory.
London Irish director of rugby Brian Smith has no doubt his side can avoid relegation from the Aviva Premiership, despite being dragged back into the dogfight.
"Yeah, we're confident," he said. "You saw our fighting qualities today. There wouldn't be many sides give away 23 penalties and not cave in.
"We've got a few guys coming back and going into this game we were five from six so we're in a pretty good space. We're pretty annoyed, the pack's particularly disappointed."
He had no quibbles about the result, though he was frustrated by the performance of referee David Rose.
"Bath deserved their win today," he said. "They were too good for us up front.
"They're cock-a-hoop and they should be. We're disappointed because with 10 minutes to go we're seven points adrift and we're leaving here with a bonus point.
"But I would say we've seen a couple of things today that are quite remarkable. The try that the boys concocted in the second half, you don't see that every day.
"And I've been in the game for 40 years and I've never seen a penalty count go above 20 before. There's three yellow cards thrown in there and with the penalty try, that's a full house. The referee obviously saw things a little differently to the way we did."
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