The Netherlands international completed his £24 million switch from Arsenal to United shortly before the conclusion of the summer transfer window and only days before the club's first league fixture of the season against Everton.
Smalling believes the fact he had so little time to gel with his new team-mates makes the striker's tally of 15 goals already this season all the more impressive.
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Van Persie was on fine form again on Saturday, scoring the first goal and setting up Wayne Rooney's third as United cruised to a 3-1 victory over Sunderland.
"I saw the finish [for his goal]," Smalling told reporters. "It wasn't easy to put it in that top corner but he is a quality player.
"Obviously he only came in the summer and didn't have much of a pre-season. But he came straight into the matches and has been such a threat.
"He is putting teams on the back foot and making our job easier at the back."
Sir Alex Ferguson's side travel to south Wales to face Swansea City at the Liberty Stadium in their next league fixture on Sunday.