The Baggies maintained their unbeaten start to the Championship campaign thanks to first-half goals from Youssouf Mulumbu and Robert Koren.
The score could have been more but Ipswich keeper Richard Wright was in inspired form, pulling off a string of fine stops, including a penalty save from Luke Moore late on.
The victory saw West Brom move level on points with Middlesbrough and Newcastle at the top.
Exceptionally wellDi Matteo told Sky Sports: "I think at some stages we played exceptionally well. We started really strong, scored the first goal, had a couple of more chances actually.
"But I thought we were always in control of the game, I thought we played really well today."
He acknowledged Wright had an "outstanding day" for Ipswich and is positive about the coming season for the Baggies.
"I think it's going to take a little while for us to do what we want to do - we are pleased with the good start and we just want to build on it."
Keane challengeIpswich boss Roy Keane admits there is a big challenge ahead for him to turn the Tractor Boys into promotion contenders.
The defeat means his side have only picked up one point from their opening four games to sit second from bottom of the Championship.
He said: "We saw today obviously in West Brom a team that are going places and we don't look like we're going anywhere too fast, so it's a big challenge ahead."
Keane added: "I always knew that the job would be difficult but there is no getting away from the fact that it is a massive, massive challenge over the next few months. It is sink or swim for the players.
"We need to do better and I don't want to keep saying it. We don't look much of a goal threat and we are giving bad goals away. That is a recipe for trouble so it is going to be very, very hard.
"But it can be done. You have to believe that we can turn it around.
"The Championship season is very long and you have to believe that we can get up to speed - sooner rather than later.
"Against Albion we gave a couple of bad goals away and we need to do better."