Owen scored his 100th goal against David on Saturday, and, despite his disappointment, the Hammers keeper offered a 'well done' at the end of the game.
He says: "I congratulated Michael on his goal - but I wanted to squeeze him a bit harder.
"I obviously didn't want him to score his 100th goal against me but he finished well, and fair play to him."
But David thinks that Jermain will be getting his own 'ton up' headlines in the years to come and adds: "I hope so for his sake; size wise there is not much between them and I think Jermain has got more power in his finishing.
"He has got more pace, but the proof of the pudding will be in the tasting, and as long as we can help him to improve, which I try and do in training myself, then he has got a chance."
David reckons that Jerzy Dudek, his Polish opposite number, made a point saving performance for Liverpool, and says: "He has done well. I was watching what he was doing and I don't think he did anything particularly wrong apart from one kick.
"He saved the shots he had to save apart from our goal, obviously, but it would have been nice to have made it a bit more difficult for him on a couple of chances to get the second goal, but he has done what he had to do to keep them in the game and in the end it was worth a point to them.
"The fact that we have made him make the saves is a bonus. For all the plaudits we got at Manchester United I don't think Barthez was overworked but against Liverpool their keeper has had a lot to do so it is a definite plus that we are creating chances.
"We could have won the Liverpool game and we could have won the Arsenal game - that's four points we would have had to take us near to them.
"But the overall performance was rewarding for me as part of the team and for the West Ham followers, definitely.
"We had many opportunities to extend our lead and the fact that they have scored a minute before injury time was a bad blow.
"They are a good team, let's be fair, and the fact that they put four international forwards on at the end meant that it was going to be difficult for us. It seemed as if they had five or six attackers at certain times but we did 99% of it right - it was just disappointing that they scored so late."
As for the controversy about that goal, when Emile Heskey appeared to control the ball with his hand, David says: "I couldn't tell if there was a handball, the ball has gone over and Nigel has gone up with Emile, the ball has dropped, and there was a body in front of me so as soon as I have come across the ball is flying past me.
"The way the goal was scored is a bit scrappy; they didn't rip us apart and people are looking left and right for excuses.
"These things happen unfortunately, but we have chances to extend the lead and their keeper has played particularly well, so it is a good result in one respect, and disappointing in another."
West Ham have come through the toughest period of the season so far without defeat, and David adds: "Glenn said if we can go through this period without losing that will see us right. It is a bit of a contradiction in terms but the best thing is that we are disappointed we haven't won more games, and had you said that before December people might have laughed."
West Ham have the joint best home defensive record in the league, along with Chelsea and Fulham, and David adds: "I think the defence is communicating a lot, which is going to help, and if the lads in front of me can do that we will keep it tight.
"As a team we did very well defending, and that is very positive."