Everton boss Roberto Martinez rued some missed chances from the Blues that could have gotten them all three points.
"I think West Ham started better than us. For the first 20 minutes we were coming to terms with the game and we put emphasis on wanting to be solid.
"Our performance against Sunderland was exciting to watch and today we had the right mindset to be tested defensively.
"Their goal is disappointing from our point of view. It's a great finish from Lanzini but he has too much space on the edge of the box.
"From that point on we became really strong. In the second half, we nullified their threat and I felt a winner was coming.
"I was delighted with the reaction but a little bit disappointed we couldn't get all three points with the amount of quality we had going forward."
Martinez was happy with John Stones' marshalling of the defence in the absence of club captain Phil Jagielka.
"It was a really interesting challenge for John because it wasn't just about defending - it was about leading that back four," he added.
"We had five defenders injured today. John had to lead the defence - and that's where I was most impressed.
"We had Tim Howard and Gareth Barry sandwiching that back four but there were very few Premier League appearances when you look at Brendan Galloway and Ramiro Funes Mori.
"I thought he was immense in the way you have to defend a striker like Andy Carroll, then take responsibility in the way he started the play out from the back. It was a magnificent performance."
He also commented on goalscorer Romelu Lukaku, and acknowledged his record-tying performance.
"I was pleased with the the equaliser, but also a little bit disappointed not to get the win with the quality we showed.
"Rom's record against West Ham is impressive. He is a very determined young man and he's capable of scoring against anyone."