Lukaku has made a strong start to life at Old Trafford following his £75m ($96m) summer switch from Everton, scoring four goals in three games – including one in the club's 4-0 victory over Swansea Cityat the Liberty Stadium on 19 August.
However, the Belgium striker was starved of touches during the match, and Pardew said he was guilty of being static when possession turned over to United.
"Lukaku needs to improve at Man Utd on when they regain possession," he told Sky Sports.
"His movement today was not good enough, to go short or long, to play quick. He needs more of that [movement] and he'll get more touches.
"There were times when the ball changed hands to United and he was static. He needs to think a little bit quicker but when the chance comes, he doesn't miss. He's a great finisher.
"We were talking earlier about [Ruud] van Nistelrooy, Teddy Sheringham and Zlatan Ibrahimovic. He needs to get some of that cleverness about where to be without the ball.
"He's at the best place to learn that because he's going to be watching the videos with Jose Mourinho after the game."
United took the lead against Swansea through Eric Bailly on the stroke of half-time, before a late flurry of goals saw Lukaku, Paul Pogba and substitute Anthony Martial all get on the scoresheet.
The win saw the Red Devils continue their 100% start to the season after the 4-0 thrashing of West Ham on the opening weekend.
"The word that describes the team now is confident," Mourinho was reported as saying by the BBC.
"At the moment, everything is going in our favour – but it's not always motorway – you find difficult roads and roadworks."
United next face 2015/16 Premier League champions Leicester City at Old Trafford on 26 August.