He said: 'All I will say is that we kept possession much further up the park than this side.'
Souness claimed that Black-burn's caution on Saturday was necessary. He said: 'I thought that tactically we played the right way. We have to be happy with a draw against a team fancied to win the Championship.
'Liverpool try to lure you out and catch you with their pace. It might not have been a great game to watch but we felt we got it right.'
Thompson replied in kind: 'They paid us the compliment of getting men behind the ball. So should we then go gung-ho and start running behind them? That is what they wanted us to do. We are more clever than that.'
Amid the strangled football there were some inspiring moments and none greater than Owen's goal with his one telling touch in the first half, when he not only outjumped but outmuscled Henning Berg.
Thompson was left in no doubt about Owen's feelings at being substituted as Liverpool tried to rally after Matt Jansen's equaliser.
He said: 'If he had been happy I would have worried about his character. But I have to look at the bigger picture, the games we have coming up.'
Souness and Thompson did not exactly fall into each other's arms at the end, but a handshake did take place before and after the proceedings.
Thompson said: 'We are both professionals. I was going to make sure there was a handshake. He has great respect for Liverpool and I have the same respect for Blackburn.'