Sterling, but Allen’s shot put paid to any comeback.
The result leaves Liverpool fifth in the Premier League table on 57 points with six games of the season to go, one point ahead of Southampton in sixth. Manchester City sit in fourth, on 61 points, with third-placed Manchester United a further four points ahead.
This win against a disjointed Newcastle was far from a return to the fluid form that the Reds discovered at the start of 2015.
Yet with Manchester City stalling above them, and three fixtures against teams in the bottom seven to follow, it was a result to fuel optimism after back-to-back league defeats against Manchester United and Arsenal.
Meanwhile, Sterling is embroiled into another controversy over photos that show him taking a pain-releasing substance known as nitrous oxide.
Images published by UK tabloid The Sun appeared to show the 20-year-old England forward taking the legal substance, also known as laughing gas.
Rogers said he would talk to Sterling about the photos. “I don’t think it is something you should be doing, it’s as simple as that,” said Rodgers.
The incident comes after Sterling admitted rejecting a new £100,000-a-week Liverpool contract.
“We want players here who are super-professional and focused on their football – I know he is,” added Rodgers.
“It’s not just on the field, it’s off the field as well but I will speak with him on it and we’ll move on.
“Young players make mistakes. As long as they learn from them, that is what is important.”
According to the BBC, Nitrous oxide is often used in surgery and dentistry for its anaesthetic effects but it is also a popular legal high as it can make people feel relaxed, euphoric and giggly.