Richard Hill's men looked set to collect a third win of the Aviva Premiership season until a try three minutes from time saw the home side ensure the points were shared.
Head Coach Hill admitted his team paid the price for sitting back and trying to defend the lead and needed to find the right mental attitude to finish off games.
And Samoan star Rasmussen agreed saying the Warriors must all take individual responsibility for mistakes for the collective good of the team before they return to league action later in the month.
"We are just not clinical at crucial times," said Rasmussen. "That is the story of two or three games now this season and we have got to address it.
"We should have really won at Newcastle, but due to a lack of accuracy and being able to kill off teams we are letting games slip.
"We need to be more accurate at the smaller things. We need to take responsibility for executing our roles and then collectively it will click.
"We are bitterly disappointed to let that try in so late in the game having defended so well, it was a similar scenario to Wasps last week," added Rasmussen.
"We have just got to get better. We will spend the week looking very hard at the video and what went wrong. We then go from there - we have got to be hard on ourselves.
"The two points could yet be crucial and anything you get on the road is a good result in the Aviva Premiership.
"We will stay positive as a squad, work hard this week and look forward to the game with Stade Francais on Thursday when we can move forward."
Tickets for the Amlin Challenge Cup opening game with Stade Francais are on sale from the Warriors Box Office. Call 01905 454183 or click HERE