"The higher the level of opponent, if you press in a disorganized fashion, then you will get picked through and we have got to be conscious of that", he said.
British Prime Minister Theresa May said she had exchanged football shirts with Plenkovic when they met on Tuesday.
Croatia have needed penalty shoot-outs to overcome Denmark and Russian Federation in the knockout stage.
Croatia has come into existence as a country for example and the Three Lions opposition have also reached a semi-final in that time, losing to hosts and eventual winners France at the 1998 World Cup.
"Health has to be number one, but to play for the Croatian team, to play in the World Cup semi-final, I do not need to even say that I will be giving it 300% to be fit".
On the Federation Internationale de Football Association world rankings Croatia are 20th with England at 12th.
While Croatia possess arguably the best central midfield pairing in the tournament in Real Madrid's Luka Modric and Barcelona's Ivan Rakitic, Southgate's language does not indicate he is about to bring in Eric Dier as an additional defensive midfielder alongside Jordan Henderson. You feel really safe and secure, as opposed to before we came out, nobody knew what to expect.
- England has not beaten two European nations in a single World Cup since 1982, when it beat Czechoslovakia and France.
Lovren continued: "I have all respect for Harry Kane". Should he score, he will become just the third player to score on all seven days of the week for England, after Wayne Rooney and Frank Lampard.
With an average age of 26, England is one of the youngest teams at the World Cup. - Mario Mandzukic assisted Andrej Kramaric's goal against Russian Federation in the quarterfinal - he has been involved in four goals at the World Cup finals for Croatia (3 goals, 1 assist), with only Davor Suker involved in more (6).
The Three Lions are just one game away from their first final since 1966, with Croatia standing between them and a showpiece against France, who beat Belgium 1-0 this morning in the first semi-final. - Croatia scored two headers in its last match against Russian Federation - only one of its previous 29 World Cup goals was scored via a header.