Stoke had never beaten Jose Mourinho's men in 10 previous Premier League meetings, but claimed all three points on Saturday as Assaidi made the perfect impact from the bench to secure a 3-2 triumph in the 90th minute.
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The Moroccan made the switch to Mark Hughes' side from Liverpool on a season-long loan deal in August after failing to break into Brendan Rodgers' first-team plans following his move from Eredivisie outfit Heerenveen a year earlier.
Assaidi's opportunities at the Britannia Stadium have also been limited this season, with the winger making just three starts in the top flight.
But the 25-year-old is hoping that his goalscoring exploits on Saturday will see him afforded more chances to prove he is worthy of a starting spot, with the ultimate aim being to force his way into the Anfield set-up.
"Everyone wants to play, me too," Assaidi said. "The coach [Hughes] made a decision for this game, but I hope for more starts.
"For me this is good because, for a long time, I didn't play and I hope I showed that I can start.
"I hope I still have a future there [Liverpool]. I have two years more and we will see, but I'm now at Stoke and I'll do my best.
"Brendan texts me sometimes and I speak sometimes with him, but we will see what the future brings.
"I think the games that I got at Liverpool were not so many, but I did well in those games. The coach makes the decisions. If he gives me a chance, then maybe I can show what I can do."