Barnes said: "Despite what many pundits were suggesting, I think Walter Smith would have kept his job even if Everton had lost at Stoke. But they won anyway and I'm pleased for Walter.
"The players really like him, Alan Stubbs dedicated his goal to him and I'm hoping Everton's fortunes will pick up."
The former Celtic boss also points to the difficult circumstances that the Everton boss has been working under, by adding: "And to be fair to Walter he has had a horrendous injury list to contend with.
"It's not surprising that Evertonians want more from their team – that's the nature of football – and compared to previous seasons I don't think Everton are struggling that badly."