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."
He went on: "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. 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."
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. 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."