Howard was given his marching orders after bringing down Sunderland's Ki Sung-Yueng in the Toffees' Boxing Day defeat to Sunderland, and is suspended for Sunday's visit of Southampton to Goodison Park.
However, Distin has given his backing to deputy Joel Robles, and feels that his side will be in safe hands.
"We have to feel comfortable with Joel behind us," Distin told the Liverpool Echo.
"He's proved he can handle it, and anyway there is no point stressing because one player or another isn't there. We're not a one-man team.
"Joel did well when he came on in the second half. Like Bryan Oviedo he can take his chance now."
The veteran French defender insists that the goalkeeper position isn't the only area that the club is blessed with sufficient cover, believing the squad is as capable as it has ever been.
"What we've got this season, compared maybe to the one before, is that in nearly every single position we've got guys waiting to play wanting to prove they should be on the pitch," he added.
"At centre-back it's the same - there are two guys who haven't played yet and when you see the way they train you see they are giving everything to play.
"That's a team for you and that's what you need if you want to compete for something interesting and some glory at the end of the season.
"You need to be a team, not just have an 11."