The reserve connected with Ashley Young’s pass in the fourth minute of added time to cancel out former Toffees winger Alex Iwobi’s 61st-minute strike and extend Everton’s unbeaten run to five games.
While they had a first-half try disallowed for offside when Dominic Calvert-Lewin intervened in the follow-up after Idrissa Gueye’s shot hit the post, the home side struggled to show much threat throughout the contest before Beto’s final touch.
Everton manager Dyche said: “I thought we didn’t, I thought they did. I think they are a good outfit anyway and they were better than us on the night.
“Not in the end – we weren’t in big trouble, we weren’t getting rings around, just the feeling of the game. I thought we were a fraction of what we used to be.
“On the other hand, the balance of football is that in this case it goes on for 96 minutes and the mentality I’ve asked the players to continue to develop is that ruthlessness and I think that showed.
“The last 10 minutes you could feel we were knocking on the door suddenly and when we scored I wasn’t that surprised because I felt the energy and feel of the game had changed, albeit for a short period.
“I was pleased to end up going on an unbeaten run and getting a point.”
The equalizer was Beto’s first of the season and just his sixth since joining from Udinese in the summer of 2023, and Dyche said of the Guinea-Bissau international: “Brian Clough had a saying, ‘sometimes you have to get an injured one to score goal’ and I thought he was done.
“He was in the mix, he threw his head at him and it was a good header.”
Disch, whose side have climbed to 15th in the Premier League table, also said there was no update on Dwight McNeil’s injury, adding: “Hopefully it’s nothing too serious.”
Fulham took the lead through Iwobi after going close twice in quick succession in the first half when Adama Traore’s shot was parried by Jordan Pickford and Emile Smith-Roe headed over the bar.
The Cottagers, whose boss Marco Silva has also returned to his old club after managing Everton from May 2018 to December 2019, remain 10th and the Portuguese said: “Really difficult for us, the result and sometimes football is difficult for an explanation.
“Everything is not going in the direction of the team that played much better from the first minute, the only team that tried to control the game. It’s difficult for us at the moment, the players are down in the dressing room.
“We should have finished the game 2-0 but we didn’t and of course these type of games, the last minutes, can go in a way that is unfair to be honest with us. Unfortunately they score at one point and at that point we have to defend better in our field.
“But we were clearly the much better team and deserved the three points. But the reaction was really good from us – I have to look at the whole picture and that’s the reaction I wanted (after losing 3-1 at home to Aston Villa last time). Even if the result was really difficult for us, the fans should be proud of the way we played.”