West Ham lost 2-1 to Domzale away from home in the first leg of the Europa League qualifying third-round tie.
Matic Crnic put the Slovenian team in the lead from the penalty spot in the 11th minute. Mark Noble equalised for the Hammers just seven minutes later with a spot kick.
The hosts secured the win with their second goal of the match just four minutes into the second half, thanks to Crnic’s second of the evening.
Sullivan has admitted that he was confused as to why West Ham did not win the match.
However, the West Ham co-chairman is confident that Slaven Bilic’s side will overcome the deficit in the second leg.
“On Thursday, we lost 2-1 to Domzale in our UEFA Europa League third qualifying round first leg tie in Slovenia, which we all admit was not good enough,” Sullivan wrote on West Ham’s official website.
“I was certainly scratching my head to explain why we couldn't hit our usual high levels of performance, and I am sure Slaven and his coaching staff were too. We know we have to do better next week – and we will.”
Over the course of the 90 minutes at the Stozice Stadium in Ljubljana on Thursday evening, hosts Domzale had 41% of the possession, took 17 shots of which six were on target, and earned 13 corners.
Visitors West Ham had 59% of the possession, took 10 shots of which three were on target, and earned five corners.