Rocks boss Jack Pearce said the referee caused his team more problems than Havant at times in the Nyewood Lane derby - but he conceded Lee Bradbury's team deserved the win.
Bognor may appeal over ref James Durkin's first-half sending-off of Ben Swallow for a challenge with Matt Tubbs and were incensed that Hawks sub Brian Stock did not see red for an elbow on Calvin Davies in the second half.
Two goals by Matt Tubbs and one from James Hayter settled the contest, cementing the teams' positions second and second from bottom in National League South, on a day when the Rocks suffered another defensive injury blow, with Chad Field leaving the ground on crutches after a lower leg injury sustained in the second half.
Pearce admitted it had been a tough day but said there was good spirit in the dressing room to keep on trying to improve their league position.
Asked about Swallow's red card, which many home fans thought very harsh, Pearce said: "From where I was sitting I couldn't make a decision one way or the other. It was obvious the referee had a very good view but subsequent video evidence shows it could have been quite a harsh decision.
"What I said to the team before the game is that we see officials in the Premier League, who are the best, make poor decisions, so you can't expect much better when they're four divisions lower. So it was most important that we did not let any decision by the referee influence the way we played the game. But obviously when you get reduced to ten men through one of those decisions, that has a major impact on the game.
"If the boy deserved to go, fine. But the video shows he actually made contact with the ball. That's all I can tell you and we'll have to wait and see how we finish up on that one. It also shows later in the game when Calvin was floored that it was rather a strong use of the elbow. That's what the assistant referee reported to the match official but he decided to think that from his view it was a coming-together rather than violent conduct even though the assistant referee informed him in his opinion it was illegal use of the elbow. That's the facts - make of that whatever you will."
Asked whether the Rocks would appeal against Swallow's red, the manager said: "It's something we will look at but you have to demonstrate that the referee has made a clear and obvious mistake and sometimes the videos at this level do not demonstrate that. So we'll have to look at it and see once we slow it down if we can prove it conclusively, and if we feel we have a chance, then we will go for it.
"I'm more upset with what their player did and got away with, especially when it was reported (to the referee) by his assistant who he obviously didn't wish to trust."
Pearce had no qualms over Havant heading back along the A27 with the three points. He said: "I don't think we played that well because football's about creating chances before the opposition. I thought Havant deserved to win. They started the game better than us, got on the front foot earlier, worked very hard to shut us down and stop us playing and they achieved that.
"What people maybe wouldn't notice from the terraces was the wind had a major influence on the game and we were against it in the first half which made it very difficult to clear your lines.
"But the most important thing was we were reduced to ten men very early and I thought we gave a good account of ourselves with ten men. There were times in the game you wouldn't have known we had ten men. The referee has had a major influence on the game today. He might be right, he might be wrong, all I know is he has caused us more problems at times than Havant did."
Keeper Dan Lincoln was named MoM after a string of excellent saves. Pearce said: "He played very well. He's a good-quality keeper."
On the Rocks' bid to try to climb away from the wrong end of the National League South, Pearce said: "Today's results have made it more difficult. But there's a good spirit in the camp and we'll keep working.
"One of the biggest worries is that one of our best players over the past month has been Chad Field and he's got a bad injury. Every time I sign a player they get injured and that makes it very difficult to get a settled side. We've now got six players injured and in a small squad that makes it very difficult. We don't know the extent of Chad's injury yet. He'll have to have a scan. He could be out for a while."
Pearce said the long-running search for a goalscorer would continue, but would not necessarily be any easier now the new year had arrived.