The Welsh government will press ahead with the introduction of a Covid pass for nightclubs and big sporting events despite only getting its policy through the Senedd because a technical issue meant an opponent could not cast his vote.

The Conservative member Gareth Davies was trying to vote remotely against the scheme but failed to connect to the debating chamber in Cardiff via Zoom, allowing the Labour-led government to win the vote 28-27.

Representatives of clubs and bars are calling for the vote to be re-run but the government said the new law, which will make holding a Covid pass compulsory for people to get into venues including nightclubs and major sporting events, would come into force.

The Welsh first minister, Mark Drakeford, said the vote was an “extraordinary” moment, but added: “The way the vote is conducted is not for the government, that is for the parliament. It is members’ responsibilities to make sure they are in the chamber or on Zoom.”

Speaking to the BBC, he said: “What was really extraordinary was the fact that opposition parties were not prepared to support this simple measure which will help to keep people safe from coronavirus.”

The Welsh government says the measure, due to come into force on Monday, is needed because of rising Covid rates, especially among young people.

The opposition parties in the Senedd, the Tories, Plaid Cymru and the Liberal Democrats, voted against the pass on Tuesday evening. It looked as if the vote was heading for a tie, which would have meant the law being blocked.

Seconds before voting time, one of the Tories in the chamber could be heard telling the Llywydd – the presiding officer – Elin Jones, that a colleague could not vote. She replied that every opportunity had been given to him to be present remotely to vote, including giving him her own personal phone number. The vote went ahead without him.

In a statement, she said: “A member was not present for the vote on proposals for Covid passes. I gave every opportunity for the member to be present … but the member was unable to be contacted.

“For members to vote in the Senedd, they must be present, either in the chamber or on Zoom. It is a member’s responsibility to give themselves sufficient time to secure their Zoom connection in time for voting, just as it is for any member travelling to the Senedd to vote.”

On Wednesday, Davies said: “I’m deeply upset, frustrated and angry at last night’s events and my inability to cast a vote against vaccine passports. IT challenges meant that I was unable to access the voting system. I was working and representing the group at the Conservative party conference and I would have been able to vote remotely if I’d have been able to access the remote voting tools. Concerns have been raised with the Senedd’s ICT department.”

None of the opposition parties have said they feel the vote ought to be re-run.