Harry Kane claimed England’s performance was “not good enough” as they succumbed to France, with the manager Gareth Southgate critical of his team’s game management after playing almost all the second period against 10 men.

The visitors had drawn level courtesy of Kane’s penalty early in the second half, with the Italian officials using the video assistant referees to confirm the award of the spot kick and the dismissal of Raphaël Varane, who was deemed not to have made an attempt to play the ball. That system is expected to be trialled in the FA Cup and League Cup next season, and could be implemented in the Premier League after the 2018 World Cup.

Yet, while neither manager complained at the video officials’ intervention, England’s inability to make inroads against depleted opponents, and tendency to present France with opportunities, left them infuriated. “Scoring twice in France should be enough,” said Kane, who captained the side. “We have got to find a way to win that. We just weren’t good enough. They were getting too much space in vital areas, even with 10 men. We want to be brave and play from the back and mistakes will happen. It’s disappointing. We were in the driver’s seat but we didn’t step it up another gear. Not good enough.”

While England remain comfortable leaders of their World Cup qualifying group, they have lost in Germany and France, and conceded two late goals to draw 2-2 with Spain in their high-profile friendlies under Southgate. The manager is using those fixtures as an education for a relatively inexperienced side.

“We’ve been competitive in all three games for long periods of time,” he said after seeing England concede three for the first time since late 2012. “But I think we’ve had to play at our absolute limit to stay in all three of the matches, which has shown in the latter stages of those games. The three games have provided a different test.

“With Spain it was their ability to keep the ball better than us, and we were chasing, chasing, chasing. Today we kept the ball better than France at times but, physically, the demands their players impose on you meant we had problems and that led to tiredness, which is one of the reasons for the mistake for the third goal. Those teams are the best. In the last few years we’ve not got anywhere near those teams when it’s come to tournaments and finals, so that’s why we need to play them. We need to see the reality of where we are, to test yourself against the best, so you don’t mask where you are in terms of a team.

“We should have got a result. In the space of 90 minutes we saw the things we’re very good at. With the ball we caused a lot of problems, looked a threat, created good openings, took our first goal very well. And equally saw the things we have to get better at. Defending as a team, and managing the game once France went down to 10. You have to control possession and stay calm, but we looked more anxious while they stepped up. We didn’t manage that period of the game as well as we need to. Part of that was because we tired. We put a huge amount into the game to try and press and deal with the physical capabilities France had, and it was a problem for us all night, their pace and athleticism.”

On the use of the video assistant referees, Southgate added: “I’ve not seen it again but, from my initial view, I thought it was the right call. It looked a clear penalty and therefore a sending off. I assume the referee wanted to make sure. If he’s got that technology to do that, then a sensible decision. Clearly, even with video, not every decision will be 100%. You won’t get every decision right. There’ll still be an element of one person’s judgment in that.”