The Gunners went down 2-1 at White Hart Lane despite Nicklas Bendtner pulling a late goal back after Danny Rose and Gareth Bale had given Spurs a two-goal lead.
Arsenal peppered the Tottenham goal but found goalkeeper Heurelho Gomes in inspired form and they now find themselves six points behind leaders Chelsea in the Barclays Premier League with four games to play.
Manager Arsene Wenger admitted after the game the north London side's title aspirations were badly hit by the loss, something echoed by Van Persie.
He told www.arsenal.com: "I don't think Chelsea will drop more than six points now."
The defeat was compounded by Thomas Vermaelen sustaining a calf strain which will keep the defender out for two to three weeks.
Van Persie, though, believes the fact Arsenal have remained in contention until this stage of the season underlines the improvement they have made in the last 12 months.
"Definitely, if you look at last year," he added. "No-one really expected this. But when you are this close you really want to win it. When you don't do that it is frustrating.
"It felt good and I am happy to be back. But when you are there and your team is behind you want to do something to help them.
"Unfortunately I could not do that last night."
Wenger introduced the Holland striker in the 68th minute and he made an immediate impact, inspiring his side forward but ultimately he was frustrated by Gomes.
The 26-year-old was thwarted by the Spurs keeper on more than one occasion when he chested down Abou Diaby's chip and volleyed goalwards before producing a perfectly-placed free-kick that was destined for the top corner.
However, both efforts saw Gomes produce stunning saves while also denying Sol Campbell's goalbound header as time ran down.
Van Persie believes Gomes' obstinacy stood between the Gunners claiming something from the game and thus keeping their title aspirations alive.
"Yes, especially the first one.
"I expected that to go in but somehow he saved it which is crazy. The free-kick was going straight into the top corner and he saved that as well. Those were big moments.
"It is a thin line between winning and losing. We had some good chances, they had some too. I felt we deserved maybe a draw from tonight.
"If you look at the second half we had a number of good chances and their keeper made a couple of unbelievable saves."
Wenger later reiterated Vermaelen is likely to miss the rest of the season while Denilson is a doubt for the trip to Wigan on Sunday.
He told TV Online: "We have to assess Denilson a little bit.
"He has a tight groin. I don't think we lost anyone else from last night [apart from Vermaelen]. I have no more news about him today. But it looks like three weeks and that means the season is over for him."
However, there was better news about Van Persie and there does not appear to have been any adverse reaction following his return.
"He came back very well," the Frenchman added.
"We have to check him today and we see how he responds to that. It was a massive gamble as he had not played.
"But we'll see how he is and hopefully he'll get a few games now."