Shawcross didn't see action last night.
Hodgson said: "When we were looking for another centre-half to add to our squad we thought he was the right man to bring in.
"His training performances have been very good and he seems to have fitted in quite well. He knows a lot of the Manchester United players anyway.
"I have got to say I have been quite happy, as I have often been in the past, because when I have brought in players who maybe haven't been a part of my squad before, they seem to have settled in easily.
"That is also a credit to Wayne Rooney and the other senior players that they make them feel comfortable.
"They make them feel at home; they encourage them to give the type of performances in training that got them the chance in the first place."