Tottenham won 2-0, though Hodgson insists he was pleased with the visitors' performance.
The manager said, "I thought that if we had just kept that a little bit longer to 0-0 or the 1-0 (if it was going to come) to just 10 or 15 minutes later, then maybe the last 15 or 20 minutes they would've had a little bit more concern for some of our attacking moves.
"(Hugo) Lloris made two very good saves, one from Patrick van Aanholt and one from Wilfried Zaha - Christian Benteke almost scored with a header. So I think they would've been worried a little bit at 1-0 but at 2-0, I suppose, that margin gave them some comfort.
"It has obviously been a great evening for them but we certainly played our part; no surrender and didn't make life easy for them."
Pre-match, Tottenham put on a musical performance and firework display to welcome in the new era for the north London club, and despite being rival's on the night, Hodgson could appreciate what has been built in White Hart Lane's place:
"It is outstanding; I can understand why there has been so much hype around it - they must be extremely proud to have created a stadium like this for their team to perform in."