It was a disappointing performance by Bolton after their memorable draw in the UEFA Cup against Bayern Munich in midweek but fatigue set in after only two days' rest.
"This match was maybe a bridge too far in terms of it being our sixth in 17 days," said Megson after the 0-0 draw.
"We have travelled a lot. Physically it is hard work but mentally it is even more so.
"I thought we looked a tired unit, running on empty.
"While Middlesbrough have been team bonding we have been flying over Europe, trying to get a result against one of the best sides around.
"It is hard trying to get yourself up all the time for games. We did not show enough quality in the last third against a tight defensive unit."
He said: "There has been a good spirit among the squad. You could see that when we were away.
"Some of the tasks we put them through was reflected in the way they dug in today.
"They've been through waterfalls and up rock faces. They were put in situations where they've had to rely on team-mates.
"They are the qualities you need on a cold, horrible day in Bolton."
Southgate praised his defenders for putting in a solid shift.
"It was a tough scrap," said the Middlesbrough boss. "These are the games where you have to roll your sleeves up and I thought we did that.
"It was not a particularly attractive game to watch. But we came with the intention of trying to win it and we looked a threat on the break at times.
"We deserved a clean sheet as we defended well as a team. We showed the character needed to get a point."