Fianna Fáil leader Michael Martin has said party has not found the right formula to be successful in the Midlands North West constituency.
Its strategy of running two candidates in the constituency could result once again lead to the party missing out there.
Anne Rabbitte and Brendan Smith are both on the Fianna Fáil ticket.
The Green Party's Saoirse McHugh could be on course to take one seat - along with Mairead McGuinness of Fine Gael.
Others like Sinn Féin's Matt Carthy and Independent Luke 'Ming' Flanagan are also vying for a seat.
An exit poll gave Brendan Smith and Anne Rabbitte 6% and 3% respectively.
But Brendan Smith got 0% among 18 to 24-year-old voters.
It has also suggested a big jump in support for The Green Party, with three of their European candidates in contention.
However the European election counts for Ireland's three constituencies will not start until Sunday morning.
A Europe-wide embargo means results cannot be declared until 10.00pm on Sunday night.
Mr Martin told Newstalk there are lessons for his party to learn.
"In the European election, we've come from a low base... I think we'll definitely win one seat in Ireland South, and we're definitely in competition for the second seat there.
"There's not a vote counted", he said.
"Obviously in Midlands North West we haven't cracked that yet in terms of the formula required."
"European elections are different... we'll wait and see - there's not a vote counted yet.
"But historically if you look at European polls, they vote differently to general elections and locals - personalities and high profile people tend to do well".
On the the Green surge, he said: "I pay tribute to them.
"Of course there are lessons and no more than myself Eamon Ryan has ploughed a lonely furrow for the last eight years when he [had] a terrible defeat like ourselves in 2011 but he stuck with it and he deservers credit for that".
"Of course we will learn and we will evaluate the outcome of this.
"But so far in terms of the tallies coming in, we have reason to be hopeful that we will do very well - not very well, but do well - in the locals".
He also suggested Taoiseach Leo Varadkar could be facing a worse local election performance than Enda Kenny.
He also commented on whether he could be Taoiseach after the next election:
🎬 "Who would have thought that Leo Varadkar would preside over a worse local election result than Enda Kenny?" @MichealMartinTD believes he can be the next Taoiseach after #Election2019 pic.twitter.com/nGtZmp7Fl0
— NewstalkFM (@NewstalkFM) May 25, 2019