The Hammers won the game on penalties after scores had finished 2-2 at fulltime.
Lopetegui later said: "We were able to put more minutes into the legs of the players.
"Today was the last friendly match, and one that we had to put more minutes inside the legs of the players. It was our last chance to do that, so it was important.
"This was a chance for us to win the trophy and to be ready for the first match of the season. I think that we did a lot of good things, but we have to continue improving more in the defensive phase.
"We have to continue working hard, for sure.
"The new players had the opportunity to get to know our stadium and to get to see what our fans are like. We have to say thank you to the fans for coming to the game today and supporting us - that’s very important for us.
"I’m sure we will have a fantastic atmosphere from them when we face Aston Villa next weekend. It will be a big challenge for us, and we have to be ready.
"Jarrod (Bowen) and Lucas (Paquetá) played their first minutes with us today.
"They both played their first minutes with us today, and of course, they aren’t ready for 90 minutes at the moment. That’s why today’s game was really important, and so that we can make sure all of the players are in a good place to compete against Aston Villa.
"We know that some players are heading into the new season with a small number of minutes, but this is something we have to be ready to adapt to and make sure we’re ready for the first match.
I think that we did a lot of good things, but we have to continue improving more in the defensive phase
"The players that we have signed are all going to add a lot of good things.
"They are going to need time because they are coming into a new club and Guido (Rodríguez) and Niclas (Füllkrug) haven’t had full pre-seasons before joining us, so they have to work very hard in the next couple of weeks to be ready to help us in the early weeks of the season.
"I’m very excited for the Premier League season to begin.
"We’ve been working hard during pre-season to prepare us for the first game. We are aware that we’re going to play against a strong team, but we are sure that we are going to be ready to work hard and give everything against Aston Villa.
"This is our last week to work and to involve the new players that have arrived. We know that this will be the same for all teams in the league. We’re looking forward to starting the campaign."