Neverauskas's father, who coaches youth baseball and national teams and promotes the sport in Lithuania, encouraged him to play baseball, despite it not being well known in the country. Neverauskas said there were no baseball fields in the country.[2] He attended training camps in Italy to better learn the game.[1] He attended his first MLB game in 2006 on a trip with his father. He attended MLB's European Baseball Academy in 2008 and 2009.[2]
On April 24, 2017, Neverauskas made his Major League Baseball debut for the Pittsburgh Pirates against the Chicago Cubs. He pitched two innings, allowed one run, and had one strikeout.[9] Neverauskas picked up his first Major League win on August 6, 2017, when the Pirates defeated the San Diego Padres in 11 innings. He pitched two scoreless innings, giving up two hits and striking out three.[10] He finished the season for the Pirates pitching in 25+1⁄3 innings with a 3.91 ERA. The following season, he pitched the majority of the season at the AAA level, registering an ERA of 8 for the Pirates in 25 games.
Neverauskas was designated for assignment by the Pirates on November 1, 2020, and released on November 3.[11]
Hiroshima Toyo Carp
On November 16, 2020, Neverauskas signed a one-year, $875,000 contract with the Hiroshima Toyo Carp of Nippon Professional Baseball (NPB) for the 2021 season.[12][13] He made his NPB debut on May 30, 2021, taking the loss against the Chiba Lotte Marines. He only pitched in one game in total, he was unable to produce results in the farm team. Neverauskas returned to the U.S. on October 6, 2021, and released on November 1.
On November 2, 2023, Neverauskas was drafted by the Long Island Ducks in the Ghost Hounds dispersal draft.[17] On February 23, 2024, prior to the start of the 2024 ALPB season, Neverauskas signed with the Charros de Jalisco of the Mexican League (LMB).[18]