Saint-Atienne (France): England captain Gary Cahill said his side had lacked "cutting edge" as they drew 0-0 with Slovakia and finished second in Group B to Wales.
"We tried and tried and they shut the door in our face," Cahill told ITV.
England coach Roy Hodgson made six changes to the line-up, but Cahill denied it had affected the result.
"I don't think so," he said. "We had the ball constantly, we just didn't quite have that cutting edge to open them up. In games like that you need something little bit special.
"We obviously tried to bring fresh legs in there, it's very difficult to play this intense and in this heat and I think we looked good. On another day we should win."
A dejected England midfielder Dele Alli (centre) walks past Slovakian players after the Euro 2016 match in Saint-Etienne on Monday. Pic/AFP
Cahill agreed that the opening 1-1 draw with Russia had ultimately cost England dear. "Of course. We may as well move on, we know we're second in the group now and we know we've got a huge game coming up."
England left-back Bertrand said, "It was frustrating not to get the win which I thought the we deserved. They defended in numbers and were resilient, and unfortunately we couldn't unlock the door. We remain very positive in our overall performance in this game and in previous games.
"Hopefully when we come up against teams in the next stages, they will hopefully give us more space."