Middlesbrough were beaten 2-0 at the Riverside on Tuesday evening.
Boro were beaten 2-0 by the Blues at the Riverside on Tuesday evening, bringing an end to their run in the Capital One Cup.
Karanka’s side were undone by two moments of quality by Roberto Martinez’s side, but were far from being thoroughly outclassed by their Premier League opponents.
And Southgate says he will have learned that he has a very good squad for the Championship, but that he will need to freshen things up if promotion to the top tier is achieved.
“I think he’ll take a lot from the whole cup run,” he told Sky Sports.
“The fact that they competed at Old Trafford, the fact they held their own here tonight [against Everton].
“He’ll know he hasn’t quite got that level of quality, he’s got a very strong squad for the Championship but not to challenge a team like Everton.”
With them now out of the cup, focus will turn back to the league for Karanka’s side.
They are currently second in the Championship table, level on points with Derby in third place and just two points behind leaders Brighton.
The league is wide open, then, with Burnley and Hull in fourth and fifth also eyeing those top two automatic promotion places.
With Ipswich Town, who are seventh in the table, up next for Karanka’s side, he will be hoping that his side can swiftly turn their focus back to returning to winning ways after the loss to the Toffees.