Messi was introduced early in the second period and the hosts improved as a result, with the Argentina star inspiring an eventual equaliser, picking out Munir El Haddadi late on.
"We have the squad and the players to be a great team and not depend on anyone, like it always used to be at Barca", Messi added.
"When we entered the closing stages of the game, we had faith and belief in ourselves even though they are one of the best teams in the world".
"Last year we hardly conceded goals but now teams are scoring against us with their first attempt".
Messi and Busquets started Saturday's 1-1 draw in LaLiga on the bench, with Valverde having an eye on a trip to Tottenham in the Champions League.
Wissam Ben Yedder volleyed home a third to wrap up the game before half-time - his sixth goal in three games.
Surprisingly, Leganes stunned the champions 2-1 in a midweek La Liga match despite Phillipe Coutinho giving the visitors the lead. "It's absolutely my responsibility".
Ahead through a Philippe Countinho goal, top of the table Barcelona looked in cruise control against bottom club Leganes who have just one point from their first five matches this season. Iñaki Williams went through but took too long to get his shot away from the edge of the six-yard box and was shepherded out to safety.
Leganes had to wait until the 30th minute for their first opening as Youssef En-Neysri broke into the box and picked out Rubén Pérez, who fired straight at goalkeeper Marc-Andre Ter Stegen. "We didn't expect them". We didn't create the chances we'd have liked. We're coming from a season when it was hard to score against us and now it's taking very little for [the opposition] to score.
- Chelsea face acid test of title ambitions against Liverpool
- Netanyahu Calls Putin, Blames Syria, Iran
- FBI To Investigate Allegations Against Brett Kavanaugh
- Google Pixel 3 XL shown off in new video
- Mourinho and Pogba have frosty exchange at Man Utd training
- Indonesia Says Sulawesi Quake Caused Tsunami
- Federal Bureau of Investigation finds body, believed to be missing NC boy
- Facebook data breach hits at least 50 mln accounts
- Typhoon Trami cripples Okinawa, threatens Japan's main islands
- Kavanaugh accusations 'all false to me,' but I could change my mind