The MP for Wirral West tweeted a link to a press release and said: "Wirral Labour can't be trusted" at 15:51 GMT on Tuesday.
Posts on the social media site claimed the timing showed a lack of respect.
The MP later tweeted: "Really regret the mistiming of local election press release. Apologies."
A Conservative Party spokesman said Ms McVey had tweeted an apology and it would not comment further. Ms McVey did not attend the memorial service.
The memorial service for the 96 people who died in the tragedy was held at Anfield on Tuesday afternoon.
Relatives of those who died, as well as fans, players and club officials were among the 24,000 who attended.