The Hammers defeated Aston Villa thanks to a goal from Kevin Nolan, and their manager was happy they were able to collect all three points on their Premier League return
Kevin Nolan's goal five minutes before the break proved to be the difference between the two sides, with the hosts going close to adding to their advantage on several occasions.
"It ended up a very good day," Allardyce told BBC Sport.
"We got a win and a clean sheet. There were a lot of good performances and it was very pleasing for everyone at West Ham to get off to a very, very good start.
"James Collins coming back was very solid in defence. That gave us the platform to go on and get this victory."
Nolan's 40th minute winner initially looked as if it would be ruled out, with the assistant's flag going up for offside against Ricardo Vaz Te in the build up.
However, referee Mike Dean awarded the goal after determining that Villa's Ciaran Clark had got the final touch on the ball through to Vaz Te.
"I was thinking it was going to get chalked off immediately but then I saw Mike waving and pointing to the spot," said Allardyce.
"When you look at the VT he's clearly got it right. We started with great expectation and I think the fans have gone home happy that we've won our first home game."
He also revealed that the club are still looking to add new faces to their squad ahead of the transfer deadline at the end of August.
"We've added good quality players to the ones we already had but there are not quite enough of them," he explained.
"We have about 18 or 19 players so we probably need a couple more, three if we're good enough in the market or if we feel the player is good enough to add to our already talented squad."