Alonso fell awkwardly on his right ankle when trying to control a clearance, unchallenged, towards the end of the first half, and was immediately carried off. He was sufficiently recovered to watch the second half from the bench, and manager Rafa Benitez reported that the midfielder was confident he would face West Ham in Cardiff on Saturday.
"He thinks he will be fit," Benitez said, "but we need to wait. Tomorrow he will have a scan. He is confident and that's a positive."
Despite a comfortable win over Portsmouth, Liverpool had to be content with third place, and the qualifying rounds of the Champions League. However, they won't have to start in the middle of July, as they did this season, rather joining at the third-round stage in the second week of August.
By midway through the first half, when United scored their second goal, the game had lost its significance. Portsmouth supporters, though, had already decided to turn it into a celebration of their Premiership survival.
Indeed, when Robbie Fowler opened the scoring, the response from the home fans was Catherine Tate-esque. "We don't care," they sang. The party was the important thing.
Liverpool were largely in control, even if too many moves went into reverse under pressure from the terriers in Portsmouth's midfield.
The busy Fowler celebrated the extension of his contract by scoring his fifth goal of his second coming, seven minutes into the second half. If his first touch from Fernanado Morientes' backheel was less than assured, his second bent the ball around Dean Kiely from a dozen yards.
Soon after, though, United scored their fourth and the rest was a footnote. Peter Crouch, booed relentlessly for his Southampton connections, tapped in a rebound after Kiely pushed Djibril Cisse's cross into his path; Ognjen Koroman lurked at the far post to turn in Wayne Routledge's centre before Crouch put Cisse clear to restore some normality.
Harry Redknapp will meet Portsmouth co-owners Milan Mandaric and Alexandre Gaydamak today to discuss both his future - he wants to stay - and the purchase of more players. "They have not come here to scrap around the bottom of the league every year," Redknapp said.