The Gunners narrowly failed to overturn a 4-0 first-leg deficit against the Italian side on Tuesday night, despite having had their chances widely written off beforehand.
And Van Persie expressed his pride in the manner of his side's performance and the support from the Emirates Stadium crowd throughout the match.
“I'm very proud to be a gunner tonight we gave everything we had! The fans were incredible best atmosphere I ever experienced thanks so much!” he wrote.
Van Persie is 6/1 with Paddy Power to score three or more goals against Newcastle on Monday night.
Arsenal fans may well be pleased to see the Netherlands international speak warmly of the club given the recent speculation over his future.
The Dutchman has been in sparkling form for the north London club this season, scoring 25 goals in the Premier League so far, and is reported to have attracted the interest of Real Madrid, amongst other clubs.
The Gunners are currently in fourth place in the Premier League but face a fierce battle with Chelsea to ensure qualification for Europe's elite competition next year.