When the Austrian took charge earlier in the season, it appeared as though Southampton were destined to go down.
However, an upturn in results has seen the Saints climb clear of the relegation zone. They have won three out of their last six games.
Bertrand said to reporters of Hasenhuttl: "The manager has come in and has given us an identity. He has given us a clear style of play and doesn't leave any stone unturned.
"It's a real pleasure to go to the field like that and not have people questioning each other what to do.
"When there is an argument, they are genuine arguments because everyone knows their role and will know if they haven't done something right.
"If you were to ask 100 people what Southampton's style of play was, the answers would all be similar.
"It would be that we are a high pressing team, very competitive and play some good football. Before, it might have been adrift."