Mylan's offer expired on Friday with just 40 percent of Perrigo shares tendered, below the required minimum 50 percent, ensuring victory for Perrigo Chief Executive Joseph Papa.
Mylan shares rose as much as 14.4 percent, while Perrigo shares fell as much as 10 percent.
Perrigo can re-enter the M&A arena with much less uncertainty, increasing the odds of a mid-sized to large deal, Jefferies analyst David Steinberg wrote in a note.
Reuters reported on Thursday that the Dublin-based company had held talks with Endo International Plc (ENDP.O), another Ireland-based drugmaker.
Healthcare deals worth a record $477 billion had been announced by the end of October, according to Thomson Reuters data, as companies consolidate to cut costs and gain scale.
Perrigo, with a large portfolio of consumer products, infant formulas and over-the-counter generic topical drugs, has long been seen as a takeover target.
To convince investors to rebuff Mylan's offer, Perrigo had announced job cuts and a $2 billion share buyback plan last month.
Perrigo said on Friday it would immediately start buying back shares, helping pull its stock off a more than one-year low.
Mylan Executive Chairman Robert Coury, who snubbed an offer from Teva Pharmaceutical Industries Ltd (TEVA.TA) to pursue Perrigo, said the company was ready to move on.
Mylan is well-positioned to "quickly execute on the next strategic, value-enhancing opportunities," some of which it has already identified, Coury said in a statement.
Raymond James analyst Elliot Wilbur, however, said he did not expect an immediate deal.
"Mylan won't necessarily be immediately opening up its checkbook for the next company it can buy and instead will step back, take a breather, and focus on the companies or assets it should buy," he wrote in a note.
Mylan shares were up 13.4 percent at $48.98 in afternoon trading, while Perrigo shares were down 7 percent at $145.50.
Mylan first made its interest in Perrigo public in April and went hostile in September, offering $75 plus 2.3 of its shares for each Perrigo share held.
Based on Mylan's Thursday close, the offer worked out to about $174.36 per share for Perrigo.
Reporting by Ankur Banerjee in Bengaluru; Editing by Ted Kerr and Kirti Pandey