The Hammers secured an impressive point against Manchester United at Old Trafford on Sunday and showed a spirited performance as they looked to bounce straight back from the agonising defeat against Tottenham last week.
Payet helped set up the opening goal after just two minutes when his free-kick fell perfectly for Diafra Sakho to head the ball past David de Gea.
Zlatan Ibrahimovic brought the home side level and even though Darren Randolph had to make several top saves, Ashley Fletcher could have won the game late on for the Hammers.
Slaven Bilic's side are looking to move clear of the bottom three and with more big games to come against Arsenal and Liverpool, Payet hopes to see a change in fortunes in the coming weeks.
Payet said: “Obviously it's an important point for us. It is never easy to come to Old Trafford and get a result, but that is what we have succeeded in doing.
“We came close to taking all three points at the end. So we are very happy with that.
“We played a good match last weekend at Tottenham and unfortunately we didn't take the points, but thankfully we have succeeded in getting something against United.
We are trying to put together a good little run to move ourselves a bit higher up the table into a more comfortable position.
Dimitri Payet
“Against these two tough teams, and we know what they are capable of - we've showed that we can compete at this level.
“We are trying to put together a good little run to move ourselves a bit higher up the table into a more comfortable position.”
Payet has enjoyed the opportunity to play in a new system which Bilic has brought into the team in recent weeks and feels the season will look a lot different when the team get back on the winning trail.
Payet added: “Obviously when the results aren't going your way it's difficult to find too much joy in the matches.
“We've had a little less of the ball than we enjoyed last season, but that's all part of the challenge at this stage and we need to accept that and we need to keep working hard.
“As I said, all it's going to take is a little bit of a good run to move us up the table and that will allow us to play with a bit more freedom.
“When you come to a place like Old Trafford you have to defend and the system is in place for perfectly good reasons.
“I'm happy right now because the decision has paid off, but yes, of course, I am more happy with the ball.”