Southampton ensured a miserable return to St Mary's for the manager, who left them in the summer, outplaying them to such an extent they deserved a wider margin of victory than that provided by Charlie Austin's first-minute goal.
Everton are seventh in the Premier League - the highest outside of those expected to compete for the title - leaves them three places above their hosts with a two-point advantage.
"I'm not worried about results, I'm worried about what I see on the pitch," the manager told reporters.
"How we start the game, have difficulties to be organised defensively and stop the opponents. I'm worried because the wake-up call, how we played in first half, to concede a goal after one minute: that cannot happen.
"It's incredible. You start a game to control a game and we didn't; we had bad defending positions for the cross. That (goal) made it difficult and a different game.
"The whole first half was not good. (We had) problems with (Southampton's) strikers, and that's strange because we know how they play. We need to be sharp, react fast to second balls. But we had some good chances in the first half; the shot from (Idrissa) Gueye needs to be on target."