They fought back from a 34-14 deficit to snatch a dramatic 38-34 home victory over Hull KR, with both sides finishing the Super League tussle with 12 men. The Reds had Lee Jewitt sent off in the last minute along with Rovers forward Adam Walker after a punch-up.
Veivers said: "It's been a long drought since our last win and I will enjoy this result. We spoke at half-time when we were 10 points down that we had the ability to win the game if we protected our goal-line."
He added: "The problem was we let in another 10 points early in the second half. We conceded some soft tries and did well to score 38 points but to concede 34 is still not acceptable. It's a massive result for the club. We could have gone on to concede 50 points when we went behind 34-14 but we scored some really nice tries."
Veivers paid tribute to Martin Gleeson on his debut after almost two years out, a spell which included an 18-month drugs ban imposed when he was at Hull.
"He looked a bit rusty understandably but did well in the second half," Veivers said. "I had put Mark Sneyd under the pump in the last two weeks but he showed he has the ability to be a good footballer."
Rovers coach Craig Sandercock was frustrated with the mistakes that his team repeatedly made after putting themselves in a winning position.
Sandercock said: "We were playing really well but then made far too many errors and gave away penalty after penalty. It's very disappointing but our discipline cost us. Con Mika was man of the match last week but this week he dropped two crucial balls. When things are not going well you don't get the bounce of the ball and we lost the penalty count 9-2."
Sandercock was unhappy with a disallowed Dale Ferguson try just before the break when Greg Eden was adjudged to have obstructed Jack Murphy.
"I thought the bloke just knocked it on and we scored," said Sandercock.