The first exit poll published after voting ended on Sunday showed a lead for the Russian-backed opposition led by Viktor Yanukovich, the former prime minister.
But the Party of the Regions says a lack of polling stations and polling booths prohibited many voters from casting their ballot.
Vasili Dzarty a spokesman for the Party of the Regions, said: "It is obvious that the people in power are trying to do everything to make sure that people do not vote."
Our Ukraine party is the ruling party.
"They are scared of losing," he said.
The opposition Tymoshenko bloc has also cited irregularities.
Aleksander Turchino, the spokesman for the Tymoshenko Bloc, said: "In some places too there weren't enough ballot boxes either and they have already all been filled."
In addition to the three main parties contesting the elections, there are 42 other parties on the ballot and elections for local, regional and mayoral posts have been running concurrently.
This proved too confusing for Maria Kolometya, standing outside her polling station in Kiev's Golden Gate district.
"Have you ever seen a ballot form this long? It runs to several metres. Who can possibly work their way through all that?" she said.
But while acknowledging "some organisational problems", most other parties and Western observers have given the vote a largely clean bill of health.
Yezhi Buzek, a former Polish prime minister and one of the European Parliament's observers at the election, said: "This is a great day for Europe and for Ukraine.
The length of the ballot paper
had some voters foxed
"We have found here a different country from that 15 months ago, as now democracy has become true here."
This election is also seen as a first major test of the political parties that emerged out of the December 2004 Orange Revolution.
The man declared the winner in that flawed election was Viktor Yanukovich, who now heads the Russia-leaning Party of the Regions, which is strong in the industrial east of the country.
But after the Constitutional Court overturned that 2004 result, the man now president, Viktor Yushchenko, won rerun elections and took office.
Yet his Europe-leaning party, Our Ukraine, which is based largely in the west of the country, has been competing for votes with the equally pro-West party of his charismatic former colleague, Yulia Tymoshenko.
The first exit poll, conducted by three Ukrainian research institutes among 20,000 voters, also predicted the Regions Party would score 33.3%. In a second exit poll conducted by the Ukrainian Sociology Service, he was seen getting 27.5%.
Yulia Tymoshenko's bloc came second with a share of the vote forecast between 21.6 and 22.7%.
Early exit polls have Viktor
Yanukovich in the lead
Kiev-based analysts say none of the parties will have enough seats to form a majority and coalitions are likely to emerge.
Our Ukraine is expected to go into talks with the Tymoshenko Bloc, while some say the shape of a future government has already largely been worked out between them.
Political analyst Tatiana Maskova said: "It makes sense, as both parties have much the same support base and outlook, although Yulia's is more radical economically."
While she was prime minister following the Orange Revolution, Tymoshenko's re-privatisation campaign - taking back state assets sold allegedly for a song by previous governments and privatising them again - caused jitters among many investors and was instrumental in Yushchenko eventually firing her.
However, the Tymoshenko Bloc has so far been reluctant to comment on any talk of a coalition forming.
"Putting together a coalition agreement is something a little more serious than going round to see someone for a cup of coffee," says Turchino. "The invitation is part of Our Ukraine's election campaign tactics."
Another coalition scenario, though controversial, could emerge between bitter rivals Yushchenko and Yanukovich, but this has not been popular with Yushchenko's voters.
"You cannot have a coalition of cats and dogs," says Our Ukraine voter and pensioner Petrov Fedorovich from Kiev.