But Leicester, much changed before Wednesday's Champions League quarter-final at Atletico Madrid, never looked comfortable.
"We know it looks like the Leicester from last season, with all the strength, with all the spirit", the Dutchman said.
Craig Shakespeare finds himself pondering the possibility of resting players at Goodison Park to protect them for a huge occasion next week. Maybe that's a reason, I don't know. "1-0 up, 2-1 down and, okay, 2-2 after 20 minutes it was not what we expect at the beginning".
Everton are already missing Seamus Coleman, Ramiro Funes Mori and Yannick Bolasie for the rest of this season. The Belgian striker now has a goal in all eight of Everton's games at Goodison Park this year.
Explaining Vardy's upturn in fortunes, the Leicester boss said: " I think it is more a case of what the team has done for Jamie - and I think he would be the first to appreciate that.
"He had a hard time when he was not playing because it's a different role".
"I don't think so at all".
"Of course he's normally still disappointed if he's not starting".
"We weren't aggressive enough and didn't have enough intent to go and attack the ball, so from that point of view it was more of how we defended as a team".
Kashmir: Water level in River Jhelum crosses 'flood declaration' mark in Srinagar
With rains continuing to pound most parts of the Valley, the administration here is gearing up for the possibility of flood. The incessant rains have triggered landslides at multiple places on 294 km Srinagar-Jammu highway leading to its closure.
The Toffees came into the game in great form on home soil of late, while Leicester were looking for a seventh straight win in all competitions since Craig Shakespeare was installed as Claudio Ranieri's successor until the end of the season.
" Everton have some very good offensive players but in general it was the set plays that were the most disappointing because ultimately they have won the game on two of those", he said.
That is not to say Leicester have no chance of progression - the six wins that lead into defeat on Merseyside suggested they are getting back to somewhere close to their best.
The win takes Everton level on points with Arsenal but the north London club have three games in hand on Koeman's side going into the final two months of the season.
"We have to make sure we're ready for each football match".
Koeman hopes to persuade star duo Lukaku and Ross Barkley - whose own deal has just over a year to run - to remain with Everton, but could not make any promises to the supporters.
The France worldwide has displayed the best pass accuracy in the squad this season, at 90% in the Premier League.
After a comparatively subdued opening to the second half, Everton extended its lead as Leicester once more failed to defend a corner.