Despite the defeat, Rodgers said he was pleased with what he saw from his charges.
Rodgers, back in the Premier League for the first time since losing his job at Liverpool in October 2015, looked to be opening his Foxes tenure with a battling point after Jamie Vardy cancelled out Troy Deeney's fifth-minute opener - but Andre Gray ruined his day when he pounced for an injury-time victor at Vicarage Road.
I have always been a big advocate of a British league with Celtic and Rangers in.
Gerard Deulofeu's whipped free-kick allowed Deeney to steal in front of Wes Morgan and flick a close-range header past Schmeichel, although he may have been marginally offside.
Leiecester, meanwhile, struggled to get their attacking going in the first half as Jamie Vardy cut a frustrating figure in the attack.
And a minute later the Foxes were level and it is the type of goal seen many times from them over the past few seasons.
Ndidi hit the woodwork with a mishit cross as Leicester cranked up the pressure and they equalised in the 75th minute, Vardy racing onto Youri Tielemans' throughball in trademark style to beat Foster.
"That's something we'll get the more we work together".
"I have got a good idea from watching the team in terms of that the needs are for the summer", he said.
"I made a lot of good friends down there". I was pleased despite not getting the result.
If he can come in and add some goals then we could be on the way to another treble.
Clearly that would give Rangers resources far beyond what we are now able to generate.