The Football Association also earlier indicated Rashford's absence was only a precautionary measure, but the Manchester United forward was conspicuous by his absence from the first session at Spartak Zelenogorsk's stadium.
"He had faith in me to play me against Malta for my debut and I can only thank him for that and ever since then I have kicked on and done well".
England were given a boost on Friday as Marcus Rashford returned to full training.
"I said to all of the team before the game, "I expect to see mistakes [against Costa Rica] and if I don't there'd probably be a problem because we won't be trying to be as good as we might".
"I mean the goal was world-class, really, but he's teasing defenders by the touchline and his performance wasn't ideal, but he was enjoying his football and that was great to see". It seems likely that Jordan Pickford will be in goal rather than Jack Butland, while Harry Maguire will be preferred for the left centre-back spot.
Lingard, scorer of important goals for his club in FA Cup and EFL Cup finals at Wembley, continued: "I think you have just got to embrace the moments".
England's training ground is a 10-minute drive from their hotel in the resort of Repino, which is 29 miles north-west of St Petersburg.
Walker, 28, accepted he was ready to play whatever role was required for England, although his preference is right-back.
England have won just one match in their last two World Cups and Southgate said: "We hope we can send people to work the following day having enjoyed our matches. It's the way I've been brought up by my family", he added.
"My friend's brother used to play here at St Petersburg and he said the city was very attractive, so it will be nice to go and see it".