The French side sealed a 2-1 win at Stamford Bridge in the second leg of their last-16 clash to wrap up a 4-2 aggregate win and book their place in the quarter-finals.
The result leaves Chelsea with just the FA Cup to focus on, with the Blues currently languishing in 10th place in the Premier League table.
However, former Chelsea man Vialli wants to see the west London side step up their performances between now and the end of the season.
Speaking on BT Sport after the game, Vialli said: “A good club shows its strength in these kinds of situations. There’s nothing to play for apart from the FA Cup.
“They need to finish the season on a high. It’s important – for themselves, for the club, for the fans, so they can really pick themselves up after this match.
“Getting fourth is almost impossible – but it’s still achievable so they have to try.”
Zlatan Ibrahimovic set up Adrien Rabiot in the 16th minute as PSG went 3-1 up on aggregate.
Chelsea pulled one back in the 27th minute thanks to Diego Costa’s smart finish.
But after Costa went off injured, Ibrahimovic converted an Angel di Maria cross in the 67th minute to secure PSG’s progress to the last eight.
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