The Hammers will face the six-time Europa League winners in their Round of 16 – starting with a trip to Spain on Thursday.
West Ham suffered a narrow defeat at Anfield but have produced a much improved performance in recent weeks and created enough chances to return to London with another victory over the Reds this season.
Pablo Fornals, Manuel Lanzini and Michail Antonio all passed up good scoring opportunities, days after Moyes criticized his forwards for lacking creativity and clear decision-making at Southampton.
If they can add the finishing touches on Thursday, West Ham could cause a surprise in Europe.
“Can we take encouragement for Sevilla? Definitely,” Moyes said.
“It’s easy for me to say that but in the end we didn’t get any points but I think we deserved something today. Someone told me coming in that we had more shots on goal in first half today than anyone since Jurgen took over and I didn’t think we were good in the first half.
“There were some good things from us and we are trying to continue. We narrowly beat Liverpool 3-2 at the London Stadium, we narrowly lost 1-0 today so there are signs we are getting a little closer to where we would like to be to challenge the top teams and Liverpool is certainly one of them. ”
With Liverpool having faced Sevilla in European competition under Klopp, Moyes took a moment to pick the German’s mastermind and try to get the upper hand.
“I was asking Jurgen about Sevilla and he was telling me different things,” Moyes said.
“I was trying to get some advice as he knows what it’s like but overall we’re having a great week [coming up] and we did a lot of good things yesterday that could have earned us a point.