WATCH: Parisse backs Ireland to pip England
The 34-year-old No.8 was speaking following a 19-56 drubbing by the Irish on Saturday, having lost 15-46 to England in Rome the previous week.
The two tournament favourites are due to meet in what many anticipate to be a Grand Slam decider at Twickenham on March 17 – which is also the national day of Ireland's patron St Patrick.
"Personally, for me having played against them both it was more difficult against Ireland," said Parisse.
"I like the way they play."
But Italy's head coach Conor O'Shea said potentially serious injuries to star centre Robbie Henshaw – who had to have oxygen administered after coming down on his shoulder when scoring his second try – and prop Tadgh Furlong, who felt a tightening of his hamstring early on, could hinder Ireland.
"If you ask me now, will Ireland win [against England]? I would say, depending on their injuries," said Irishman O'Shea.
"They are big losses to the team but at the same time they won't lose here [at Lansdowne Road against Wales or Scotland].
"They will have stiffer tests because their opponents will hold on to the ball, unlike us.
"I cannot see any other option than this title race going down to the England match on March 17th," added the 47-year-old former Ireland fullback.
Ireland captain Rory Best was pleased with Parisse's compliment but insisted his side could still improve.
"I think it's always nice when you get a compliment from an opposing captain," said Best, who scored one of Ireland's eight tries.
"But we'll look at this game and we'll see there are a lot of things we can do a lot better.
"There are things we'll be pleased with but it's a nice compliment from a class player, but we'll judge ourselves with how we go,"
Ireland head coach Joe Schmidt – bidding for a third Six Nations title but first Grand Slam since taking over in 2013 – insisted he was optimistic of winning the title.
"You do feel that you're in with a chance when you can get those first two wins," said Schmidt.
"Especially with an away win first up [15-13 over France].
"We haven't lost a Six Nations game at home in the five years I've been involved – we drew once with Wales post World Cup but that was when I felt we needed rebuilding.
"There's a real benchmark there that we can hopefully defend.
"Although we probably had a couple of knock-backs injury-wise"
Schmidt admitted the Welsh would be a far tougher nut to crack than a porous Italian defence.
"Wales will be a whole different scenario," he added.
"They are very attacking as a defensive side and they squeeze you and force errors.
"For us where we are now, we've already started thinking forward because we don't really have too much time to reflect," added the 52-year-old New Zealander.
As for Italy, O'Shea swore that he had seen enough over the first two matches to convince him they could win at least one match this campaign.
"We've done enough in these three halves [discounting the first-half against Ireland where they shipped 28 points to none] to show we can do something in this Six Nations.
"We showed today we had the match fitness, otherwise we wouldn't have scored those tries. But you also need fitness of the mind and fitness of intensity," he added.
Agence France-Presse
