The club took issue with remarks the official allegedly made towards Lallana in a 2-1 defeat at Everton on December 29.
Both the Football Association and the referees' governing body, the Professional Game Match Officials Limited (PGMOL), found that Clattenburg did not have a case to answer.
Reflecting on the scrutiny the England international faced, Davis said: "I think for the first day he was a bit like 'why is everyone coming for me?' He made a remark after the game, conversations happen and the end result was the end result.
"But anyone that knows Adam knows that first of all he is a good pro, a good lad, a good person.
"I think after the first day or two he realised that himself, that he hadn't done anything wrong, he shouldn't be feeling anything negative about himself and then he banged a goal in against Burnley. That kind of epitomises where he is mentally."
Davis expects Lallana to continue improving following his rise from League One to England honours.
He added: "As he gets older, he has got that bit of belief that what he was doing in the Championship he can step up and do at a higher level.
"I think as well when he first had the Southampton armband, you could see it kind of held him back a little bit. But now the way he has matured, he doesn't find that a weight now. Again, that comes down to belief.
"The manager (Mauricio Pochettino) coming in at the time he did and working closely with him has helped.
"The way he has been treated from the very top of the club with his new contract has helped the way he has developed, with the England call-up probably that final turning point in his head.
"He has a real opportunity to really become a very good player at this level, so he is obviously great to have around the place."
